Symmetries in Lagrangian Field Theory
NASA Astrophysics Data System (ADS)
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
"Lagrangian" for a Non-Lagrangian Field Theory with N=2 Supersymmetry.
Gadde, Abhijit; Razamat, Shlomo S; Willett, Brian
2015-10-23
We suggest that at least some of the strongly coupled N=2 quantum field theories in 4D can have a nonconformal N=1 Lagrangian description flowing to them at low energies. In particular, we construct such a description for the N=2 rank one superconformal field theory with E(6) flavor symmetry, for which a Lagrangian description was previously unavailable. We utilize this description to compute several supersymmetric partition functions. PMID:26551100
Conditions for the existence of a Lagrangian in field theory
Farias, J.R.
1982-12-15
The necessary and sufficient conditions for a given set of n second-order field equations to be derivable from a variational principle of Hamilton's type were derived recently by Santilli. An alternative form is given which makes practical verification less tedious, and permits a direct construction of the Lagrangian.
Generalization of the extended Lagrangian formalism on a field theory and applications
Deriglazov, A. A.; Rizzuti, B. F.
2011-06-15
Formalism of extended Lagrangian represents a systematic procedure to look for the local symmetries of a given Lagrangian action. In this work, the formalism is discussed and applied to a field theory. We describe it in detail for a field theory with first-class constraints present in the Hamiltonian formulation. The method is illustrated on examples of electrodynamics, Yang-Mills field, and nonlinear sigma model.
Peierls brackets in non-Lagrangian field theory
NASA Astrophysics Data System (ADS)
Sharapov, A. A.
2014-10-01
The concept of Lagrange structure allows one to systematically quantize the Lagrangian and non-Lagrangian dynamics within the path-integral approach. In this paper, I show that any Lagrange structure gives rise to a covariant Poisson bracket on the space of solutions to the classical equations of motion, be they Lagrangian or not. The bracket generalize the well-known Peierls' bracket construction and make a bridge between the path-integral and the deformation quantization of non-Lagrangian dynamics.
NASA Technical Reports Server (NTRS)
Guertin, R. F.; Wilson, T. L.
1977-01-01
To illustrate that a relativistic field theory need not be manifestly covariant, Lorentz-invariant Lagrangian densities are constructed that yield the equation satisfied by an interacting (two-component) Sakata-Taketani spin-0 field. Six types of external field couplings are considered, two scalars, two vectors, an antisymmetric second-rank tensor, and a symmetric second-rank tensor, with the results specialized to electromagnetic interactions. For either of the two second-rank couplings, the equation is found to describe noncausal wave propagation, a property that is apparent from the dependence of the coefficients of the space derivatives on the external field; in contrast, the noncausality of the corresponding manifestly covariant Duffin-Kemmer-Petiau spin-0 equation is not so obvious. The possibilities for generalizing the results to higher spin theories involving only the essential 2(2J + 1) components for a particle with a definite spin J and mass m are discussed in considerable detail.
The Lagrangian-space Effective Field Theory of large scale structures
NASA Astrophysics Data System (ADS)
Porto, Rafael A.; Senatore, Leonardo; Zaldarriaga, Matias
2014-05-01
We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of extended objects in Lagrangian space. In LEFT the resulting finite size effects are described using a multipole expansion parameterized by a set of time dependent coefficients and organized in powers of the ratio of the wavenumber of interest k over the non-linear scale kNL. The multipoles encode the effects of the short distance modes on the long-wavelength universe and absorb UV divergences when present. There are no IR divergences in LEFT. Some of the parameters that control the perturbative approach are not assumed to be small and can be automatically resummed. We present an illustrative one-loop calculation for a power law universe. We describe the dynamics both at the level of the equations of motion and through an action formalism.
The Lagrangian-space Effective Field Theory of large scale structures
Porto, Rafael A.; Zaldarriaga, Matias; Senatore, Leonardo E-mail: senatore@stanford.edu
2014-05-01
We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of extended objects in Lagrangian space. In LEFT the resulting finite size effects are described using a multipole expansion parameterized by a set of time dependent coefficients and organized in powers of the ratio of the wavenumber of interest k over the non-linear scale k{sub NL}. The multipoles encode the effects of the short distance modes on the long-wavelength universe and absorb UV divergences when present. There are no IR divergences in LEFT. Some of the parameters that control the perturbative approach are not assumed to be small and can be automatically resummed. We present an illustrative one-loop calculation for a power law universe. We describe the dynamics both at the level of the equations of motion and through an action formalism.
The recursion relation in Lagrangian perturbation theory
Rampf, Cornelius
2012-12-01
We derive a recursion relation in the framework of Lagrangian perturbation theory, appropriate for studying the inhomogeneities of the large scale structure of the universe. We use the fact that the perturbative expansion of the matter density contrast is in one-to-one correspondence with standard perturbation theory (SPT) at any order. This correspondence has been recently shown to be valid up to fourth order for a non-relativistic, irrotational and dust-like component. Assuming it to be valid at arbitrary (higher) order, we express the Lagrangian displacement field in terms of the perturbative kernels of SPT, which are itself given by their own and well-known recursion relation. We argue that the Lagrangian solution always contains more non-linear information in comparison with the SPT solution, (mainly) if the non-perturbative density contrast is restored after the displacement field is obtained.
NASA Astrophysics Data System (ADS)
Battista, Emmanuele; Dell'Agnello, Simone; Esposito, Giampiero; Di Fiore, Luciano; Simo, Jules; Grado, Aniello
2015-09-01
We first analyze the restricted four-body problem consisting of the Earth, the Moon, and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L4 or L5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L4 or L5. It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the long-distance form of the potential among two masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order 2 mm, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 m, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 m per orbit. The latter is a cumulative effect accurately measured at the centimeter level through the lunar laser ranging positioning technique. Thus, it is possible to study a new laser ranging test of general relativity to measure the 7.61 m correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. Performing such an experiment requires controlling the propulsion to precisely reach L1, using an instrumental accuracy comparable to the measurement of the lunar geodesic precession, and understanding systematic effects resulting from thermal radiation and multibody gravitational perturbations. This will then be the basis to consider a second-generation experiment to study deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system.
Covariant Noncommutative Field Theory
Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.
2008-07-02
The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.
Relativistic Lagrangian displacement field and tensor perturbations
NASA Astrophysics Data System (ADS)
Rampf, Cornelius; Wiegand, Alexander
2014-12-01
We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the basic Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the Lagrangian frame. These techniques are (a) from defining a local set of Eulerian coordinates embedded into the Lagrangian frame; (b) from performing a specific gauge transformation; and (c) from a fully nonperturbative approach based on the Arnowitt-Deser-Misner (ADM) split. The latter approach shows that this decomposition is not tied to a specific perturbative formulation for the solution of the Einstein equations. Rather, it can be defined at the level of the nonperturbative coordinate change from the Lagrangian to the Eulerian description. Studying such different techniques is useful because it allows us to compare and develop further the various approximation techniques available in the Lagrangian formulation. We find that one has to solve the gravitational wave equation in the relativistic analysis, otherwise the corresponding Newtonian limit will necessarily contain spurious nonpropagating tensor artifacts at second order in the Eulerian frame. We also derive the magnetic part of the Weyl tensor in the Lagrangian frame, and find that it is not only excited by gravitational waves but also by tensor perturbations which are induced through the nonlinear frame dragging. We apply our findings to calculate for the first time the relativistic displacement field, up to second order, for a Λ CDM Universe in the presence of a local primordial non-Gaussian component. Finally, we also comment on recent claims about whether mass conservation in the Lagrangian frame is violated.
Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories
NASA Astrophysics Data System (ADS)
Tronko, Natalia; Brizard, Alain J.
2015-11-01
A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.
Recursive solutions of Lagrangian perturbation theory
NASA Astrophysics Data System (ADS)
Matsubara, Takahiko
2015-07-01
In the standard perturbation theory (SPT) of self-gravitating Newtonian fluid in an expanding universe, recurrence relations for higher-order solutions are well known and play an important role both in practical applications and in theoretical investigations. The recurrence relations in Lagrangian perturbation theory (LPT), however, have not been known for a long time. Recently, two different kinds of recurrence relations in LPT have been proposed in limited cases. In this paper, we generalize those methods, and most generally derive the recurrence relations, which are capable of including any initial condition in general models of cosmology. The fastest-growing modes in the general relations are identified, and simplified recurrence relations with accurate approximation for the time dependence are obtained.
Using Lagrangian perturbation theory for precision cosmology
Sugiyama, Naonori S.
2014-06-10
We explore the Lagrangian perturbation theory (LPT) at one-loop order with Gaussian initial conditions. We present an expansion method to approximately compute the power spectrum LPT. Our approximate solution has good convergence in the series expansion and enables us to compute the power spectrum in LPT accurately and quickly. Non-linear corrections in this theory naturally satisfy the law of conservation of mass because the relation between matter density and the displacement vector of dark matter corresponds to the conservation of mass. By matching the one-loop solution in LPT to the two-loop solution in standard perturbation theory, we present an approximate solution of the power spectrum which has higher order corrections than the two-loop order in standard perturbation theory with the conservation of mass satisfied. With this approximation, we can use LPT to compute a non-linear power spectrum without any free parameters, and this solution agrees with numerical simulations at k = 0.2 h Mpc{sup –1} and z = 0.35 to better than 2%.
Deconstructing field-induced ketene isomerization through Lagrangian descriptors.
Craven, Galen T; Hernandez, Rigoberto
2016-01-27
The time-dependent geometrical separatrices governing state transitions in field-induced ketene isomerization are constructed using the method of Lagrangian descriptors. We obtain the stable and unstable manifolds of time-varying transition states as dynamic phase space objects governing configurational changes when the ketene molecule is subjected to an oscillating electric field. The dynamics of the isomerization reaction are modeled through classical trajectory studies on the Gezelter-Miller potential energy surface and an approximate dipole moment model which is coupled to a time-dependent electric field. We obtain a representation of the reaction geometry, over varying field strengths and oscillation frequencies, by partitioning an initial phase space into basins labeled according to which product state is reached at a given time. The borders between these basins are in agreement with those obtained using Lagrangian descriptors, even in regimes exhibiting chaotic dynamics. Major outcomes of this work are: validation and extension of a transition state theory framework built from Lagrangian descriptors, elaboration of the applicability for this theory to periodically- and aperiodically-driven molecular systems, and prediction of regimes in which isomerization of ketene and its derivatives may be controlled using an external field. PMID:26778728
String perturbation theory and effective Lagrangians
Klebanov, I.
1987-09-01
We isolate logarithmic divergences from bosonic string amplitudes on a disc. These divergences are compared with 'tadpole' divergences in the effective field theory with a cosmological term, which also contains an effective potential for the dilation. Also, corrections to ..beta..-functions are compared with variations of the effective action. In both cases we find an inconsistency between the two. This is a serious problem which could undermine our ability to remove divergences from the bosonic string.
Lagrangian statistical model for transport in highly heterogeneous velocity fields.
Le Borgne, Tanguy; Dentz, Marco; Carrera, Jesus
2008-08-29
We define an effective Lagrangian statistical model in phase space (x, t, v) for describing transport in highly heterogeneous velocity fields with complex spatial organizations. The spatial Markovian nature (and temporal non-Markovian nature) of Lagrangian velocities leads to an effective transport description that turns out to be a correlated continuous time random walk. This model correctly captures the Lagrangian velocity correlation properties and is demonstrated to represent a forward model for predicting transport in highly heterogeneous porous media for different types of velocity organizations. PMID:18851594
Effective metric Lagrangians from an underlying theory with two propagating degrees of freedom
Krasnov, Kirill
2010-04-15
We describe an infinite-parametric class of effective metric Lagrangians that arise from an underlying theory with two propagating degrees of freedom. The Lagrangians start with the Einstein-Hilbert term, continue with the standard R{sup 2}, (Ricci){sup 2} terms, and in the next order contain (Riemann){sup 3} as well as on-shell vanishing terms. This is exactly the structure of the effective metric Lagrangian that renormalizes quantum gravity divergences at two loops. This shows that the theory underlying the effective field theory of gravity may have no more degrees of freedom than is already contained in general relativity. We show that the reason why an effective metric theory may describe just two propagating degrees of freedom is that there exists a (nonlocal) field redefinition that maps an infinitely complicated effective metric Lagrangian to the usual Einstein-Hilbert one. We describe this map for our class of theories and, in particular, exhibit it explicitly for the (Riemann){sup 3} term.
NASA Astrophysics Data System (ADS)
You, Setthivoine
2015-11-01
A new canonical field theory has been developed to help interpret the interaction between plasma flows and magnetic fields. The theory augments the Lagrangian of general dynamical systems to rigourously demonstrate that canonical helicity transport is valid across single particle, kinetic and fluid regimes, on scales ranging from classical to general relativistic. The Lagrangian is augmented with two extra terms that represent the interaction between the motion of matter and electromagnetic fields. The dynamical equations can then be re-formulated as a canonical form of Maxwell's equations or a canonical form of Ohm's law valid across all non-quantum regimes. The field theory rigourously shows that helicity can be preserved in kinetic regimes and not only fluid regimes, that helicity transfer between species governs the formation of flows or magnetic fields, and that helicity changes little compared to total energy only if density gradients are shallow. The theory suggests a possible interpretation of particle energization partitioning during magnetic reconnection as canonical wave interactions. This work is supported by US DOE Grant DE-SC0010340.
Field theory for string fluids
NASA Astrophysics Data System (ADS)
Schubring, Daniel; Vanchurin, Vitaly
2015-08-01
We develop a field theory description of nondissipative string fluids and construct an explicit mapping between field theory degrees of freedom and hydrodynamic variables. The theory generalizes both a perfect particle fluid and pressureless string fluid to what we call a perfect string fluid. Ideal magnetohydrodynamics is shown to be an example of the perfect string fluid whose equations of motion can be obtained from a particular choice of the Lagrangian. The Lagrangian framework suggests a straightforward extension of the perfect string fluid to more general anisotropic fluids describing higher dimensional branes such as domain walls. Other modifications of the Lagrangian are discussed which may be useful in describing relativistic superfluids and fluids containing additional currents.
Augmented Lagrangian Method for Constrained Nuclear Density Functiional Theory
Staszczak, A.; Stoitsov, Mario; Baran, Andrzej K; Nazarewicz, Witold
2010-01-01
The augmented Lagrangian method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme Hartree-Fock-Bogoliubov (CHFB) variant. The ALM allows precise calculations of multidimensional energy surfaces in the space of collective coordinates that are needed to, e.g., determine fission pathways and saddle points; it improves accuracy of computed derivatives with respect to collective variables that are used to determine collective inertia and is well adapted to supercomputer applications.
Transport Theory from the Nambu-Jona-Lasinio Lagrangian
NASA Astrophysics Data System (ADS)
Marty, R.; Torres-Rincon, J. M.; Bratkovskaya, E.; Aichelin, J.
2016-01-01
Starting from the (Polyakov-) Nambu-Jona-Lasinio Lagrangian, (P)NJL, we formulate a transport theory which allows for describing the expansion of a quark-antiquark plasma and the subsequent transition to the hadronic world —without adding any new parameter to the standard (P)NJL approach, whose parameters are fixed to vacuum physics. This transport theory can be used to describe ultrarelativistic heavy-ion reaction data as well as to study the (first-order) phase transition during the expansion of the plasma. (P)NJL predicts such a phase transition for finite chemical potentials. In this contribution we give an outline of the necessary steps to obtain such a transport theory and present first results.
Augmented Lagrangian formulation of orbital-free density functional theory
Suryanarayana, Phanish Phanish, Deepa
2014-10-15
We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas–Fermi–von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.
Regular reduction of relativistic theories of gravitation with a quadratic Lagrangian
Bel, L.; Zia, H.S.
1985-12-15
We consider those relativistic theories of gravitation which generalize Einstein's theory in the sense that their field equations derive from a scalar Lagrangian which, besides the matter term, contains a linear combination of the Ricci scalar, its square, and the square of the Ricci tensor. Using a generalization of a technique which has been used to deal with some dynamical systems, we regularly and covariantly reduce the corresponding fourth-order differential equations to second-order ones. We examine, in particular, at a low order of approximation, these reduced equations in cosmology, and for static and spherically symmetric interior solutions with constant density.
Costa-Quintana, J. Lopez-Aguilar, F.
2012-08-15
We analyze the conditions of the electromagnetic potentials for systems with electric and magnetic charges and the Lagrangian theory with these potentials. The constructed Lagrangian function is valid for obtaining the field equations and the extended Lorentz force for dyonic charges for both relativistic particles in vacuum and non-relativistic entities in solids. In a second part, with the one-body Hamiltonian of independent particles in external fields, we explore some dual properties of the dyonic system under external fields. We analyze the possible diamagnetic (and 'diaelectric') response of magnetic monopoles under a weak and constant electromagnetic field and the theory of Landau levels in the case of magnetic charges under strong electromagnetic constant fields. - Highlights: Black-Right-Pointing-Pointer We study the Lagrangian formalism for magnetic charges. Black-Right-Pointing-Pointer We analyze the electromagnetic potentials for dyons. Black-Right-Pointing-Pointer We study two dual properties of solid systems with magnetic charges. Black-Right-Pointing-Pointer A quantum study of solids with monopoles under electromagnetic constant fields.
Symmetries in k-Symplectic Field Theories
Roman-Roy, Narciso
2008-06-25
k-symplectic geometry provides the simplest geometric framework for describing certain class of first-order classical field theories. Using this description we analyze different kinds of symmetries for the Hamiltonian and Lagrangian formalisms of these field theories, including the study of conservation laws associated to them and stating Noether's theorem.
Quantum noncanonical field theory: Symmetries and interaction
Carmona, J. M.; Cortes, J. L.; Indurain, J.; Mazon, D.
2009-11-15
The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincare invariance in an auxiliary spacetime is found in the Lagrangian version of the path integral formulation. This invariance is contrasted with the idea of doubly (or deformed) special relativity. This analysis is then used to go from the free theory of a complex field to an interacting field theory.
Nonsymmetric unified field theory. II. Phenomenological aspects
NASA Astrophysics Data System (ADS)
Ragusa, S.
2001-04-01
The nonsymmetric unified field theory of gravitation and electromagnetism developed in a previous paper in vacuum is here supplemented by introducing the sources. The sources of the field, the matter energy-momentum tensor and the electromagnetic current, are introduced explicitly into the Lagrangian providing a close contact with elementary particle physics concepts in the linear approximation of the theory and an explicit form for the conservation laws. The theory is shown to be free of ghost-negative energy particles and tachyons as well. The equations of motion of test charged particles are established through the invariance of the interaction Lagrangian.
About non standard Lagrangians in cosmology
Dimitrijevic, Dragoljub D.; Milosevic, Milan
2012-08-17
A review of non standard Lagrangians present in modern cosmological models will be considered. Well known example of non standard Lagrangian is Dirac-Born-Infeld (DBI) type Lagrangian for tachyon field. Another type of non standard Lagrangian under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory Lagrangian. We will investigate homogenous cases of both DBI and p-adic fields and obtain Lagrangians of the standard type which have the same equations of motions as aforementioned non standard one.
NASA Astrophysics Data System (ADS)
Hebda, Piotr Wiktor
For a given Lagrangian, in general singular, containing higher order time derivatives, a dynamically equivalent Lagrangian with only first order time derivatives is constructed. A Hamiltonian structure for this first order Lagrangian is then found with the use of the Dirac theory of constraints. However, in contrast with the usual Dirac procedure the method presented here starts with the Euler-Lagrange equations of motion. It is shown that in the case of a nonsingular higher order Lagrangian, the Ostrogradsky dynamics is derived this way. Further, it is shown that ambiguities characteristic of higher order Lagrangian systems do not appear when using this construction. Also, for a given system of ODE, an equivalent first order ODE system, suitable for the construction of a Bateman type Lagrangian is given. The Hamiltonian structure of this Lagrangian is then derived with the use of the Dirac theory of constraints. The uniqueness of the structure is proven and special properties of the construction are discussed. A Hamiltonian for the Bateman Lagrangian for a damped harmonic oscillator is obtained. The system is then quantized. The Hamiltonian operator, its eigenvalues and eigenfunctions are explicitly given. The long time behavior of some observables is discussed.
Unification Principle and a Geometric Field Theory
NASA Astrophysics Data System (ADS)
Wanas, Mamdouh I.; Osman, Samah N.; El-Kholy, Reham I.
2015-08-01
In the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.
Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory
Andreussi, T.; Morrison, P. J.; Pegoraro, F.
2013-09-15
Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energy-Casimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e., variations that explicitly preserve invariants of the system, are introduced and the respective energy principle is considered. General criteria for stability are obtained, along with comparisons between the three different approaches.
Tatekawa, Takayuki
2014-04-01
We study the initial conditions for cosmological N-body simulations for precision cosmology. In general, Zel'dovich approximation has been applied for the initial conditions of N-body simulations for a long time. These initial conditions provide incorrect higher-order growth. These error caused by setting up the initial conditions by perturbation theory is called transients. We investigated the impact of transient on non-Gaussianity of density field by performing cosmological N-body simulations with initial conditions based on first-, second-, and third-order Lagrangian perturbation theory in previous paper. In this paper, we evaluates the effect of the transverse mode in the third-order Lagrangian perturbation theory for several statistical quantities such as power spectrum and non-Gaussianty. Then we clarified that the effect of the transverse mode in the third-order Lagrangian perturbation theory is quite small.
Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models
NASA Technical Reports Server (NTRS)
Buchert, T.; Melott, A. L.; Weiss, A. G.
1993-01-01
We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.
The Lagrangian formulation of strong-field quantum electrodynamics in a plasma
Raicher, Erez; Department of Applied Physics, Soreq Nuclear Research Center, Yavne 81800 ; Eliezer, Shalom; Nuclear Fusion Institute, Polytechnic University of Madrid, Madrid ; Zigler, Arie
2014-05-15
The Lagrangian formulation of the scalar and spinor quantum electrodynamics in the presence of strong laser fields in a plasma medium is considered. We include the plasma influence in the free Lagrangian analogously to the “Furry picture” and obtain coupled equations of motion for the plasma particles and for the laser propagation. We demonstrate that the strong-field wave (i.e., the laser) satisfies a massive dispersion relation and obtain self-consistently the effective mass of the laser photons. The Lagrangian formulation derived in this paper is the basis for the cross sections calculation of quantum processes taking place in the presence of a plasma.
The Lagrangian formulation of strong-field quantum electrodynamics in a plasma
NASA Astrophysics Data System (ADS)
Raicher, Erez; Eliezer, Shalom; Zigler, Arie
2014-05-01
The Lagrangian formulation of the scalar and spinor quantum electrodynamics in the presence of strong laser fields in a plasma medium is considered. We include the plasma influence in the free Lagrangian analogously to the "Furry picture" and obtain coupled equations of motion for the plasma particles and for the laser propagation. We demonstrate that the strong-field wave (i.e., the laser) satisfies a massive dispersion relation and obtain self-consistently the effective mass of the laser photons. The Lagrangian formulation derived in this paper is the basis for the cross sections calculation of quantum processes taking place in the presence of a plasma.
Quantum Field Theory, Revised Edition
NASA Astrophysics Data System (ADS)
Mandl, F.; Shaw, G.
1994-01-01
Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W± and Z° bosons had been observed and the experimental investigation of high energy electro-weak interactions was in its infancy. Nowadays, W± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen-sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro-weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical interpretation is stressed at every point and its use is illustrated in detailed applications. After studying this book, the reader should be able to calculate any process in lowest order of perturbation theory for both QED and the standard electro-weak theory, and in addition, calculate lowest order radiative corrections in QED using the powerful technique of dimensional regularization. Contents: Preface; 1 Photons and electromagnetic field; 2 Lagrangian field theory; 3 The Klein--Gordon field; 4 The Dirac field; 5 Photons: covariant theory; 6 The S-matrix expansion; 7 Feynman diagrams and rules in QED; 8 QED processes in lowest order; 9 Radiative corrections; 10 Regularization; 11 Weak interactions; 13 Spontaneous symmetry breaking; 14 The standard electro-weak theory; Appendix A The Dirac equation; Appendix B Feynman rules and formulae for perturbation theory; Index.
Kheirandish, F.; Amooshahi, M.
2008-11-18
Quantum field theory of a damped vibrating string as the simplest dissipative scalar field theory is investigated by introducing a minimal coupling method. The rate of energy flowing between the system and its environment is obtained.
Euler-Poincare reduction for discrete field theories
Vankerschaver, Joris
2007-03-15
In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed.
Generalized Lee-Wick formulation from higher derivative field theories
Cho, Inyong; Kwon, O-Kab
2010-07-15
We study a higher derivative (HD) field theory with an arbitrary order of derivative for a real scalar field. The degree of freedom for the HD field can be converted to multiple fields with canonical kinetic terms up to the overall sign. The Lagrangian describing the dynamics of the multiple fields is known as the Lee-Wick (LW) form. The first step to obtain the LW form for a given HD Lagrangian is to find an auxiliary field (AF) Lagrangian which is equivalent to the original HD Lagrangian up to the quantum level. Until now, the AF Lagrangian has been studied only for N=2 and 3 cases, where N is the number of poles of the two-point function of the HD scalar field. We construct the AF Lagrangian for arbitrary N. By the linear combinations of AF fields, we also obtain the corresponding LW form. We find the explicit mapping matrices among the HD fields, the AF fields, and the LW fields. As an exercise of our construction, we calculate the relations among parameters and mapping matrices for N=2, 3, and 4 cases.
NASA Astrophysics Data System (ADS)
Enßlin, Torsten
2013-08-01
Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms even for nonlinear and non-Gaussian signal inference problems. IFT algorithms exploit spatial correlations of the signal fields and benefit from techniques developed to investigate quantum and statistical field theories, such as Feynman diagrams, re-normalisation calculations, and thermodynamic potentials. The theory can be used in many areas, and applications in cosmology and numerics are presented.
Dual field theory of strong interactions
Akers, D.
1987-07-01
A dual field theory of strong interactions is derived from a Lagrangian of the Yang-Mills and Higgs fields. The existence of a magnetic monopole of mass 2397 MeV and Dirac charge g = (137/2)e is incorporated into the theory. Unification of the strong, weak, and electromagnetic forces is shown to converge at the mass of the intermediate vector boson W/sup +/-/. The coupling constants of the strong and weak interactions are derived in terms of the fine-structure constant ..cap alpha.. = 1/137.
I.Y. Dodin; N.J. Fisch; G.M. Fraiman
2003-02-06
The Lagrangian and Hamiltonian functions describing average motion of a relativistic particle under the action of intensive high-frequency electromagnetic radiation are obtained. In weak, low-frequency background fields, such a particle on average drifts with an effective, relativistically invariant mass, which depends on the intensity of the electromagnetic field.
Chiral Lagrangians from lattice gauge theories in the strong coupling limit
Nagao, Taro; Nishigaki, Shinsuke M.
2001-07-01
We derive nonlinear {sigma} models (chiral Lagrangians) over symmetric spaces U(n), U(2n)/Sp(2n), and U(2n)/O(2n) from U(N), O(N), and Sp(2N) lattice gauge theories coupled to n flavors of staggered fermions, in the large-N and g{sup 2}N limit. To this end, we employ Zirnbauer{close_quote}s color-flavor transformation. We prove the spatial homogeneity of the vacuum configurations of mesons by explicitly solving the large-N saddle point equations, and thus establish these patterns of spontaneous chiral symmetry breaking in the above limit.
(Non-)decoupled supersymmetric field theories
NASA Astrophysics Data System (ADS)
Di Pietro, Lorenzo; Dine, Michael; Komargodski, Zohar
2014-04-01
We study some consequences of coupling supersymmetric theories to (super)gravity. To linear order, the couplings are determined by the energy-momentum supermultiplet. At higher orders, the couplings are determined by contact terms in correlation functions of the energy-momentum supermultiplet. We focus on the couplings of one particular field in the supergravity multiplet, the auxiliary field M . We discuss its linear and quadratic (seagull) couplings in various supersymmetric theories. In analogy to the local renormalization group formalism [1-3], we provide a prescription for how to fix the quadratic couplings. They generally arise at two-loops in perturbation theory. We check our prescription by explicitly computing these couplings in several examples such as mass-deformed = 4 and in the Coulomb phase of some theories. These couplings affect the Lagrangians of rigid supersymmetric theories in curved space. In addition, our analysis leads to a transparent derivation of the phenomenon known as Anomaly Mediation. In contrast to previous approaches, we obtain both the gaugino and scalar masses of Anomaly Mediation by relying just on classical, minimal supergravity and a manifestly local and supersymmetric Wilsonian point of view. Our discussion naturally incorporates the connection between Anomaly Mediation and supersymmetric AdS 4 Lagrangians. This note can be read without prior familiarity with Anomaly Mediated Supersymmetry Breaking (AMSB).
On p-Adic Sector of Open Scalar Strings and Zeta Field Theory
Dragovich, Branko
2010-06-17
We consider construction of Lagrangians which may be suitable for description of p-adic sector of an open scalar string. Such Lagrangians have their origin in Lagrangian for a single p-adic string and they contain the Riemann zeta function with the d'Alembertian in its argument. However, investigation of the field theory with Riemann zeta function is interesting in itself as well. We present a brief review and some new results.
NASA Technical Reports Server (NTRS)
Melott, A. L.; Buchert, T.; Weib, A. G.
1995-01-01
We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.
Understanding conformal field theory through parafermions and Chern Simons theory
Hotes, S.A.
1992-11-19
Conformal field theories comprise a vast class of exactly solvable two dimensional quantum field theories. Conformal theories with an enlarged symmetry group, the current algebra symmetry, axe a key ingredient to possible string compactification models. The following work explores a Lagrangian approach to these theories. In the first part of this thesis, a large class of conformal theories, the so-called coset models, are derived semi-classically from a gauged version Of the Wess-Zumino-Witten functional. A non-local field transformation to the parafermionic field description is employed in the quantization procedure. Classically, these parafermionic fields satisfy non-trivial Poisson brackets, providing insight into the fractional spin nature of the conformal theory. The W-algebra symmetry is shown to appear naturally in this approach. In the second part of this thesis, the connection between the fusion algebra structure of Wess-Zumino-Witten models and the quantization of the Chern-Simons action on the torus is made explicit. The modular properties of the conformal model are also derived in this context, giving a natural demonstration of the Verlinde conjecture. The effects of background gauge fields and monopoles are also discussed.
Twenty-first Century Lattice Gauge Theory: Results from the QCD Lagrangian
Kronfeld, Andreas S.; /Fermilab
2012-03-01
Quantum chromodynamics (QCD) reduces the strong interactions, in all their variety, to an elegant nonabelian gauge theory. It clearly and elegantly explains hadrons at short distances, which has led to its universal acceptance. Since its advent, however, many of its long-distance, emergent properties have been believed to be true, without having been demonstrated to be true. This paper reviews a variety of results in this regime that have been established with lattice gauge theory, directly from the QCD Lagrangian. This body of work sheds light on the origin of hadron masses, its interplay with dynamical symmetry breaking, as well as on other intriguing features such as the phase structure of QCD. In addition, nonperturbative QCD is quantitatively important to many aspects of particle physics (especially the quark flavor sector), nuclear physics, and astrophysics. This review also surveys some of the most interesting connections to those subjects.
Fermion boson metamorphosis in field theory
Ha, Y.K.
1982-01-01
In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered.
Topological field theory amplitudes for A N-1 fibration
NASA Astrophysics Data System (ADS)
Iqbal, Amer; Khan, Ahsan Z.; Qureshi, Babar A.; Shabbir, Khurram; Shehper, Muhammad A.
2015-12-01
We study the partition function N=1 5D U( N) gauge theory with g adjoint hypermultiplets and show that for massless adjoint hypermultiplets it is equal to the partition function of a two dimensional topological field on a genus g Riemann surface. We describe the topological field theory by its amplitudes associated with cap, propagator and pair of pants. These basic amplitudes are open topological string amplitudes associated with certain Calabi-Yau threefolds in the presence of Lagrangian branes.
BRST-invariant Lagrangian of spontaneously broken gauge theories in a noncommutative geometry
Okumura, Y.
1996-09-01
The quantization of spontaneously broken gauge theories in a noncommutative geometry (NCG) has been sought for some time, because quantization is crucial for making the NCG approach a reliable and physically acceptable theory. Lee, Hwang, and Ne{close_quote}eman recently succeeded in realizing the BRST quantization of gauge theories in a NCG in the matrix derivative approach proposed by Coquereaux and co-workers. The present author has proposed a characteristic formulation to reconstruct a gauge theory in a NCG on the discrete space {ital M}{sub 4}{times}{ital Z}{sub {sub {ital N}}}. Since this formulation is a generalization of the differential geometry on the ordinary manifold to that on the discrete manifold, it is more familiar than other approaches. In this paper, we show that within our formulation we can obtain the BRST-invariant Lagrangian in the same way as Lee, Hwang, and Ne{close_quote}eman and apply it to the SU(2){times}U(1) gauge theory. {copyright} {ital 1996 The American Physical Society.}
Mimetic Theory for Cell-Centered Lagrangian Finite Volume Formulation on General Unstructured Grids
Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.; Christon, Mark A.
2012-07-19
A finite volume cell-centered Lagrangian scheme for solving large deformation problems is constructed based on the hypo-elastic model and using the mimetic theory. Rigorous analysis in the context of gas and solid dynamics, and arbitrary polygonal meshes, is presented to demonstrate the ability of cell-centered schemes in mimicking the continuum properties and principles at the discrete level. A new mimetic formulation based gradient evaluation technique and physics-based, frame independent and symmetry preserving slope limiters are proposed. Furthermore, a physically consistent dissipation model is employed which is both robust and inexpensive to implement. The cell-centered scheme along with these additional new features are applied to solve solids undergoing elasto-plastic deformation.
Leclercq, Florent; Jasche, Jens; Wandelt, Benjamin; Gil-Marín, Héctor E-mail: jasche@iap.fr E-mail: wandelt@iap.fr
2013-11-01
On the smallest scales, three-dimensional large-scale structure surveys contain a wealth of cosmological information which cannot be trivially extracted due to the non-linear dynamical evolution of the density field. Lagrangian perturbation theory (LPT) is widely applied to the generation of mock halo catalogs and data analysis. In this work, we compare topological features of the cosmic web such as voids, sheets, filaments and clusters, in the density fields predicted by LPT and full numerical simulation of gravitational large-scale structure formation. We propose a method designed to improve the correspondence between these density fields, in the mildly non-linear regime. We develop a computationally fast and flexible tool for a variety of cosmological applications. Our method is based on a remapping of the approximately-evolved density field, using information extracted from N-body simulations. The remapping procedure consists of replacing the one-point distribution of the density contrast by one which better accounts for the full gravitational dynamics. As a result, we obtain a physically more pertinent density field on a point-by-point basis, while also improving higher-order statistics predicted by LPT. We quantify the approximation error in the power spectrum and in the bispectrum as a function of scale and redshift. Our remapping procedure improves one-, two- and three-point statistics at scales down to 8 Mpc/h.
Altimetric Lagrangian advection to reconstruct Pacific Ocean fine-scale surface tracer fields
NASA Astrophysics Data System (ADS)
Rogé, Marine; Morrow, Rosemary A.; Dencausse, Guillaume
2015-09-01
In past studies, Lagrangian stirring of surface tracer fields by altimetric surface geostrophic currents has been performed in different mid- to high-latitude regions, showing good results in reconstructing finer scale tracer patterns. Here, we explore the pertinence of the technique in the western equatorial Pacific and in the subtropical southwest Pacific. Initial conditions are derived from weekly gridded low-resolution temperature and salinity fields based on in situ hydrographic data. Validation of the reconstructed fine-scale surface tracer fields is performed using satellite AMSRE Sea Surface Temperature data and high-resolution ship thermosalinograph data. We test two kinds of Lagrangian advection. The standard one-way advection leads to an increased error as the advection time increases, due to the missing physics, such as air-sea fluxes or non-geostrophic dynamics. A second "backward-forward" advection technique is explored to reduce this bias in the tracer field, with improved results. In the subtropical southwest Pacific Ocean, the mesoscale temperature and salinity fronts are well represented by both Lagrangian advection techniques over a short 7- to 14-day advection time, including westward-propagating features not apparent in the initial fields. In the tropics, the results are less clear. The validation is hampered by the complex vertical stratification, and the lateral stirring technique is limited by the pertinence of using geostrophic surface current fields in the tropics. We suggest that the passive lateral stirring technique is efficient in regions with moderate to high mesoscale energy, where mesoscale surface tracer and surface height fields are correlated. In other regions, more complex dynamical processes may need to be included.
Subedi, P.; Chhiber, R.; Tessein, J. A.; Wan, M.; Matthaeus, W. H.
2014-12-01
The Minimal Multiscale Lagrangian Mapping procedure developed in the context of neutral fluid turbulence is a simple method for generating synthetic vector fields. Using a sequence of low-pass filtered fields, fluid particles are displaced at their rms speed for some scale-dependent time interval, and then interpolated back to a regular grid. Fields produced in this way are seen to possess certain properties of real turbulence. This paper extends the technique to plasmas by taking into account the coupling between the velocity and magnetic fields. We examine several possible applications to plasma systems. One use is as initial conditions for simulations, wherein these synthetic fields may efficiently produce a strongly intermittent cascade. The intermittency properties of the synthetic fields are also compared with those of the solar wind. Finally, studies of cosmic ray transport and modulation in the test particle approximation may benefit from improved realism in synthetic fields produced in this way.
Hybrid conformal field theories
NASA Astrophysics Data System (ADS)
Bertolini, Marco; Melnikov, Ilarion V.; Plesser, M. Ronen
2014-05-01
We describe a class of (2,2) superconformal field theories obtained by fibering a Landau-Ginzburg orbifold CFT over a compact Khler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model, our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of linear models and comparing spectra among the phases.
Effective Field Theories from Soft Limits of Scattering Amplitudes
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav
2015-06-01
We derive scalar effective field theories—Lagrangians, symmetries, and all—from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.
NASA Astrophysics Data System (ADS)
Surana, K. S.; Reddy, J. N.; Nunez, D.
2015-05-01
The paper presents rate constitutive theories for finite deformation of homogeneous, isotropic, compressible, and incompressible thermoviscoelastic solids without memory in Lagrangian description derived using the second law of thermodynamics expressed in terms of Gibbs potential Ψ. To ensure thermodynamic equilibrium during evolution, the rate constitutive theories must be derived using entropy inequality [as other three conservation and balance laws are do not provide a mechanism for deriving constitutive theories for the deforming matter (Surana in Advanced mechanics of continuua. in preparation, 2014)]. The two forms of the entropy inequality in Ψ derived using conjugate pairs , : first Piola-Kirchhoff stress tensor and material derivative of the Jacobian of deformation and , ; second Piola-Kirchhoff stress tensor and material derivative of Green's strain tensor are precisely equivalent as the conjugate pairs , and , are transformable from each other. In the present work, we use , as conjugate pair. Two possible choices of dependent variables in the constitutive theories: Ψ, η, , and Ψ, η, , (in which η is entropy density and is heat vector) are explored based on conservation and balance laws. It is shown that the choice of Ψ, η, , is essential when the entropy inequality is expressed in terms of Ψ. The arguments of these dependent variables are decided based on desired physics. Viscoelastic behavior requires considerations of at least and (or ) in the constitutive theories. We generalize and consider strain rates ; i = 0, 1, …, n-1 as arguments of the dependent variables in the derivations of the ordered rate theories of up to orders n. At the onset, , ; i = 0, 1, …, n-1, θ and are considered as arguments of Ψ, η, and . When is substituted in the entropy inequality, the resulting conditions eliminate η as a dependent variable, reduce arguments of some of the dependent variables in the constitutive theory etc. but do not provide a mechanism to derive constitutive theories for and . The stress tensor is decomposed into equilibrium stress and deviatoric stress . Upon substituting this in the entropy inequality, we finally arrive at the inequality that must be satisfied by , and . Derivations of the constitutive theory for follow directly from , equilibrium Cauchy stress tensor, and the constitutive theory for is derived using the theory of generators and invariants. Constitutive theories for the heat vector of up to orders n that are consistent (in terms of the argument tensors) with the constitutive theories for are also derived. Many simplified forms of the rate theories of orders n are presented. Material coefficients are derived by considering Taylor series expansions of the coefficients in the linear combinations representing and using the combined generators of the argument tensors about a known configuration in the combined invariants of the argument tensors and temperature. It is shown that the rate constitutive theories of order one ( n = 1) when further simplified results in constitutive theories that resemble currently used theories but are in fact different. The solid materials characterized by these theories have mechanisms of elasticity and dissipation but have no memory, i.e., no relaxation behavior or rheology. Fourier heat conduction law is shown to be an over-simplified case of the rate theory of order one for . The paper establishes when there is equivalence between the constitutive theories derived here using Ψ and those presented in Surana et al. (Acta Mech 224(11):2785—2816, 2013), that are derived using Helmholtz free energy density Φ.
Inductive approach towards a phenomenologically more satisfactory unififed field theory
Rayski, J.; Rayski J.M. Jnr.
1985-11-01
A unified field theory constituting a fusion of the ideas of supersymmetries with general relativity and gauge theory is investigated. A Lagrangian formalism is constructed step by step; the last step consists in a marriage with Kaluza's idea of a multidimensional space-time. Our aim is not to achieve a full local supersymmetry in eleven dimensions, but rather to attain a compromise with the symmetries of the fundamental interactions either known phenomenologically, or only suspected to exist in nature.
Twistor Geometry and Field Theory
NASA Astrophysics Data System (ADS)
Ward, R. S.; Wells, Raymond O., Jr.
1991-08-01
Part I. Geometry: 1. Klein correspondence; 2. Fibre bundles; 3. Differential geometry; 4. Integral geometry; Part II. Field Theory: 5. Linear field theory; 6. Gauge theory; 7. General relativity; Part III. The Penrose Transform: 8. Massless free fields; 9. Self-dual gauge fields; 10. Self-dual space-times; 11. General gauge fields; 12. Stationary axisymmetric space-times; Special topics.
Limits on Higgs boson couplings in Effective field theory
NASA Astrophysics Data System (ADS)
Belyaev, N.; Reid, T.
2016-02-01
We review the Effective Field Theory (EFT) to make projections on physics beyond the Standard Model in the Higgs sector. We provide relations between the non-Standard Model couplings of the Strongly-Interacting Light Higgs (SILH) effective Lagrangian implemented in the eHDecay package and the corresponding terms of the spin-0 Higgs Characterisation model's effective Lagrangian used with the aMC@NLO Monte Carlo generator. Constraints on BSM couplings are determined on the basis of existing experimental limits on Higgs boson width and branching ratios.
NASA Astrophysics Data System (ADS)
Surana, K. S.; Reddy, J. N.; Nunez, Daniel
2015-11-01
This paper presents ordered rate constitutive theories of orders m and n, i.e., ( m, n) for finite deformation of homogeneous, isotropic, compressible and incompressible thermoviscoelastic solids with memory in Lagrangian description using entropy inequality in Gibbs potential Ψ as an alternate approach of deriving constitutive theories using entropy inequality in terms of Helmholtz free energy density Φ. Second Piola-Kirchhoff stress σ [0] and Green's strain tensor ɛ [0] are used as conjugate pair. We consider Ψ, heat vector q, entropy density η and rates of upto orders m and n of σ [0] and ɛ [0], i.e., σ [ i]; i = 0, 1, . . . , m and ɛ [ j]; j = 0, 1, . . . , n. We choose Ψ, ɛ [ n], q and η as dependent variables in the constitutive theories with ɛ [ j]; j = 0, 1, . . . , n - 1, σ [ i]; i = 0, 1, . . . , m, temperature gradient g and temperature θ as their argument tensors. Rationale for this choice is explained in the paper. Entropy inequality, decomposition of σ [0] into equilibrium and deviatoric stresses, the conditions resulting from entropy inequality and the theory of generators and invariants are used in the derivations of ordered rate constitutive theories of orders m and n in stress and strain tensors. Constitutive theories for the heat vector q (of up to orders m and n - 1) that are consistent (in terms of the argument tensors) with the constitutive theories for ɛ [ n] (of up to orders m and n) are also derived. Many simplified forms of the rate theories of orders ( m, n) are presented. Material coefficients are derived by considering Taylor series expansions of the coefficients in the linear combinations representing ɛ [ n] and q using the combined generators of the argument tensors about a known configuration {{\\underline{\\varOmega}}} in the combined invariants of the argument tensors and temperature. It is shown that the rate constitutive theories of order one ( m = 1, n = 1) when further simplified result in constitutive theories that resemble currently used theories but are in fact different. The solid continua characterized by these theories have mechanisms of elasticity, dissipation and memory, i.e., relaxation behavior or rheology. Fourier heat conduction law is shown to be an over simplified case of the rate theory of order one ( m = 1, n = 1) for q. The paper establishes when there is equivalence between the constitutive theories derived here using Ψ and those presented in reference Surana et al. (Acta Mech. doi:10.1007/s00707-014-1173-6, 2014) that are derived using Helmholtz free energy density Φ. The fundamental differences between the two constitutive theories in terms of physics and their explicit forms using Φ and Ψ are difficult to distinguish from the ordered theories of orders ( m, n) due to complexity of expressions. However, by choosing lower ordered theories, the difference between the two approaches can be clearly seen.
Synthetic three-dimensional turbulent passive scalar fields via the minimal Lagrangian map
NASA Astrophysics Data System (ADS)
Rosales, Carlos
2011-07-01
A method for simple but realistic generation of three-dimensional synthetic turbulent passive scalar fields is presented. The method is an extension of the minimal turnover Lagrangian map approach (MTLM) [C. Rosales and C. Meneveau, Phys. Rev. E 78, 016313 (2008)] formulated for the generation of synthetic turbulent velocity fields. In this development, the minimal Lagrangian map is applied to deform simultaneously a vector field and an advected scalar field. This deformation takes place over a hierarchy of spatial scales encompassing a range from integral to dissipative scales. For each scale, fluid particles are mapped transporting the scalar property, without interaction or diffusional effects, from their initial configuration to new positions determined only by their velocity at the beginning of the motion and a parameter chosen to accumulate deformation for the equivalent of the phenomenological "turn-over" time scale. The procedure is studied for the case of inertial-convective regime. It is found that many features of passive scalar turbulence are well reproduced by this simple kinematical construction. Fundamental statistics of the resulting synthetic scalar fields, evaluated through the flatness and probability density functions of the scalar gradient and scalar increments, reproduce quite well the known statistical characteristics of passive scalars in turbulent fields. High-order statistics are also consistent with those observed in real hydrodynamic turbulence. The anomalous scaling of real turbulence is well reproduced for different kind of structure functions, with good quantitative agreement in general, for the scaling exponents. The spatial structure of the scalar field is also quite realistic, as well as several characteristics of the dissipation fields for the scalar variance and kinetic energy. Similarly, the statistical geometry at dissipative scales that ensues from the coupling of velocity and scalar gradients behaves in agreement with what is already known for real scalar turbulence in the considered regime. The results indicate that the multiscale self-distortion of the velocity field is an important factor to capture realistically turbulent scalar features beyond low-order statistics.
Beyond mean field theory: statistical field theory for neural networks
Buice, Michael A; Chow, Carson C
2014-01-01
Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi–Peliti–Janssen formalism, are particularly useful in this regard. PMID:25243014
Probing {N}=2 superconformal field theories with localization
NASA Astrophysics Data System (ADS)
Fiol, Bartomeu; Garolera, Blai; Torrentsa, Genís
2016-01-01
We use supersymmetric localization to study probes of four dimensional Lagrangian {N}=2 superconformal field theories. We first derive a unique equation for the eigenvalue density of these theories. We observe that these theories have a Wigner eigenvalue density precisely when they satisfy a necessary condition for having a holographic dual with a sensible higher-derivative expansion. We then compute in the saddle-point approximation the vacuum expectation value of 1/2-BPS circular Wilson loops, and the two-point functions of these Wilson loops with the Lagrangian density and with the stress-energy tensor. This last computation also provides the corresponding Bremsstrahlung functions and entanglement entropies. As expected, whenever a finite fraction of the matter is in the fundamental representation, the results are drastically different from those of {N}=4 supersymmetric Yang-Mills theory.
Perturbative quantum gravity in double field theory
NASA Astrophysics Data System (ADS)
Boels, Rutger H.; Horst, Christoph
2016-04-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
NASA Astrophysics Data System (ADS)
Chu, Yi-Zen
This thesis describes theoretical physics research performed by the author mainly from Summer 2007 through Spring 2010. Two common threads run through this body of work: they involve various aspects of quantum and classical field theory; and the extensive use of Mathematica. But it otherwise spans a broad range of subjects. We first show that, contrary to claims in the literature, fermions can definitely form bound states on kink-antikinks. Next we borrow techniques from perturbative quantum field theory to calculate the effective dynamics of the n-body problem in classical General Relativity, up to O [(v/c)4] beyond Newtonian gravity, where v is the typical speed of the n compact objects. Following that, we exploit the bosonized version of quantum electrodynamics in two dimensional Minkowski spacetime to solve the backreaction problem of fermion-antifermion pair production for two "capacitor" setups, i.e. with a initial electric field localized in space. Finally, we examine the rates of fermion-antifermions pair production due to the time dependent U[1] gauge vector potential around an oscillating solenoid and that of cosmic string loops.
Singleton field theory and quantum groups
NASA Astrophysics Data System (ADS)
Lay, Yat-Lo
1997-11-01
The conventional field theory in physics is formulated under Minkowski spacetime background, which is geometrically of zero curvature. This dissertation studies the extension to spacetimes of nonzero constant curvature, namely, the anti-de Sitter spacetimes (negative curvature), and the de Sitter spacetimes (positive curvature). A field theory, singleton field theory, on anti-de Sitter spacetime is established, for only anti-de Sitter spacetime assures the vacuum stability and a lower bound for energy. First, we give a Lagrangian and Hamiltonian formulation for the spinor singleton model, and from that, we find that the dynamics of a physical singleton is determined solely by some delicate boundary conditions at spatial infinity of anti-de Sitter spacetime. This means that singleton field theory is a nonlocal field theory. We also proceed to calculate tbe Hamiltonian of the theory, and show that the physical Hamiltonian concentrates only on the boundary at spatial infinity. Singleton field theory is a gauge theory. To obtain a quantum theory of singletons, we give, based upon the Nakanishi-Ojima approach, a BRST formulation for the scalar singletons in four dimensions. This scheme can be applied to spinor models, and to singletons in other spacetime dimensions. The BRST-charge is explicitly calculated, and the nonlocal behavior of singletons is interpreted in terms of the cohomology structure of its energy-momentum tensor. Another interesting aspect of anti-de Sitter spacetime is also discussed. In three dimensional anti-de Sitter spacetime, it allows several inequivalent theories ot quantum electrodynamics. We study the one which carries spin one gauge particles. The theory has the Chern-Simons structure and its classical interaction is nonlocal. The possibility of generating local interaction from quantum anomaly is inspected. The quantum field theory in de Sitter spacetime is also investigated in this dissertation. A special feature of the theory is that here energy does not have a lower bound. According to Nachtmann and Thirring, particles could be generated, and this effect was significant only within the very early universe time scale. We study its cosmology implication by giving an estimate for the particle creation during the inflation period of the universe. The last part of this dissertation is devoted to quantum groups. We study the deformations of quantum gl(n) based on generalized symmetry. In particular, explicit calculations are given for quantum gl(3), and there one finds a very special quantum group which does not have a classical limit in the usual sense. A new set of coordinates is constructed for simplification and the implication is discussed. We adopt /hbar = c = 1 units in this dissertation unless stated otherwise.
A random field approach to the Lagrangian modeling of turbulent transport in vegetated canopies
NASA Astrophysics Data System (ADS)
Cesari, Rita; Paradisi, Paolo
2015-09-01
We present an application of a Lagrangian Stochastic Model (LSM) to turbulent dispersion over complex terrain, where turbulent coherent structures are known to play a crucial role. We investigate the case of a vegetated canopy by using semi-empirical parameterizations of turbulence profiles in the region inside and above a canopy layer. The LSM is based on a 4-dimensional Fokker-Planck (4DFP) equation, which extends the standard Thomson87 Lagrangian approach. The 4DFP model is derived by means of a Random Field description of the turbulent velocity field. The main advantage of this approach is that not only the experimental Eulerian one-point statistics, but also the Eulerian two-point two-time covariance structure can be included explicitly in the LSM. At variance with the standard Thomson87 approach, the 4DFP model allows to consider explicit parameterizations of the turbulent coherent structures as it explicitly includes both spatial and temporal correlation functions. In order to investigate the effect of the turbulent geometrical structure on a scalar concentration profile, we performed numerical simulations with two different covariance parameterizations, the first one isotropic and the second anisotropic. We show that the accumulation of scalars near the ground is due to the anisotropic geometrical properties of the turbulent boundary layer.
Towards a double field theory on para-Hermitian manifolds
Vaisman, Izu
2013-12-15
In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kähler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian manifold. The field is interpreted as a compatible (pseudo-)Riemannian metric. The tangent bundle of the manifold has a natural, metric-compatible bracket that extends the C-bracket of double field theory. In the para-Kähler case, this bracket is equal to the sum of the Courant brackets of the two Lagrangian foliations of the manifold. Then, we define a canonical connection and an action of the field that correspond to similar objects of double field theory. Another section is devoted to the Marsden-Weinstein reduction in double field theory on para-Hermitian manifolds. Finally, we give examples of fields on some well-known para-Hermitian manifolds.
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more complicated non-rational theories. Examples include critical percolation, supersymmetric string backgrounds, disordered electronic systems, sandpile models describing avalanche processes, and so on. In each case, the non-rationality and non-unitarity of the CFT suggested that a more general theoretical framework was needed. Driven by the desire to better understand these applications, the mid-1990s saw significant theoretical advances aiming to generalise the constructs of rational CFT to a more general class. In 1994, Nahm introduced an algorithm for computing the fusion product of representations which was significantly generalised two years later by Gaberdiel and Kausch who applied it to explicitly construct (chiral) representations upon which the energy operator acts non-diagonalisably. Their work made it clear that underlying the physically relevant correlation functions are classes of reducible but indecomposable representations that can be investigated mathematically to the benefit of applications. In another direction, Flohr had meanwhile initiated the study of modular properties of the characters of logarithmic CFTs, a topic which had already evoked much mathematical interest in the rational case. Since these seminal theoretical papers appeared, the field has undergone rapid development, both theoretically and with regard to applications. Logarithmic CFTs are now known to describe non-local observables in the scaling limit of critical lattice models, for example percolation and polymers, and are an integral part of our understanding of quantum strings propagating on supermanifolds. They are also believed to arise as duals of three-dimensional chiral gravity models, fill out hidden sectors in non-rational theories with non-compact target spaces, and describe certain transitions in various incarnations of the quantum Hall effect. Other physical applications range from two-dimensional turbulence and non-equilibrium systems to aspects of the AdS/CFT correspondence and describing supersymmetric sigma models beyond the topological sector. We refer the reader to the reviews in this collection for further applications and details. More recently, our understanding of logarithmic CFT has improved dramatically thanks largely to a better understanding of the underlying mathematical structures. This includes those associated to the vertex operator algebras themselves (representations, characters, modular transformations, fusion, braiding) as well as structures associated with applications to two-dimensional statistical models (diagram algebras, eg. Temperley-Lieb quantum groups). Not only are we getting to the point where we understand how these structures differ from standard (rational) theories, but we are starting to tackle applications both in the boundary and bulk settings. It is now clear that the logarithmic case is generic, so it is this case that one should expect to encounter in applications. We therefore feel that it is timely to review what has been accomplished in order to disseminate this improved understanding and motivate further applications. We now give a quick overview of the articles that constitute this special issue. Adamović and Milas provide a detailed summary of their rigorous results pertaining to logarithmic vertex operator (super)algebras constructed from lattices. This survey discusses the C2-cofiniteness of the (p, p') triplet models (this is the generalisation of rationality to the logarithmic setting), describes Zhu's algebra for (some of) these theories and outlines the difficulties involved in explicitly constructing the modules responsible for their logarithmic nature. Cardy gives an account of a popular approach to logarithmic theories that regards them, heuristically at least, as limits of ordinary (but non-rational) CFTs. More precisely, it seems that any given correlator may be computed as a limit of standard (non-logarithmic) correlators, any logarithmic singularities that arise do so because of a degeneration when taking the limit. He then illustrates this phenomenon in several theories describing statistical lattice models including the n → 0 limit of the O(n ) model and the Q → 1 limit of the Q-state Potts model. Creutzig and Ridout review the continuum approach to logarithmic CFT, using the percolation (boundary) CFT to detail the connection between module structure and logarithmic singularities in correlators before describing their proposed solution to the thorny issue of generalising modular data and Verlinde formulae to the logarithmic setting. They illustrate this proposal using the three best-understood examples of logarithmic CFTs: the (1, 2) models, related to symplectic fermions; the fractional level WZW model on , related to the beta gamma ghosts; and the WZW model on GL(1|1). The analysis in each case requires that the spectrum be continuous; C2-cofinite models are only recovered as orbifolds. Flohr and Koehn consider the characters of the irreducible modules in the spectrum of a CFT and discuss why these only span a proper subspace of the space of torus vacuum amplitudes in the logarithmic case. This is illustrated explicitly for the (1, 2) triplet model and conclusions are drawn for the action of the modular group. They then note that the irreducible characters of this model also admit fermionic sum forms which seem to fit well into Nahmrsquo;s well-known conjecture for rational theories. Quasi-particle interpretations are also introduced, leading to the conclusion that logarithmic C2-cofinite theories are not so terribly different to rational theories, at least in some respects. Fuchs, Schweigert and Stigner address the problem of constructing local logarithmic CFTs starting from the chiral theory. They first review the construction of the local theory in the non-logarithmic setting from an angle that will then generalise to logarithmic theories. In particular, they observe that the bulk space can be understood as a certain coend. The authors then show how to carry out the construction of the bulk space in the category of modules over a factorisable ribbon Hopf algebra, which shares many properties with the braided categories arising from logarithmic chiral theories. The authors proceed to construct the analogue of all-genus correlators in their setting and establish invariance under the mapping class group, i.e. locality of the correlators. Gainutdinov, Jacobsen, Read, Saleur and Vasseur review their approach based on the assumption that certain classes of logarithmic CFTs admit lattice regularisations with local degrees of freedom, for example quantum spin chains (with local interactions). They therefore study the finite-dimensional algebras generated by the hamiltonian densities (typically the Temperley-Lieb algebras and their extensions) that describe the dynamics of these lattice models. The authors then argue that the lattice algebras exhibit, in finite size, mathematical properties that are in correspondence with those of their continuum limits, allowing one to predict continuum structures directly from the lattice. Moreover, the lattice models considered admit quantum group symmetries that play a central role in the algebraic analysis (representation structure and fusion). Grumiller, Riedler, Rosseel and Zojer review the role that logarithmic CFTs may play in certain versions of the AdS/CFT correspondence, particularly for what is known as topologically massive gravity (TMG). This has been a very active subject over the last five years and the article takes great care to disentangle the contributions from the many groups that have participated. They begin with some general remarks on logarithmic behaviour, much in the spirit of Cardyrsquo;s review, before detailing the distinction between the chiral (no logs) and logarithmic proposals for critical TMG. The latter is then subjected to various consistency checks before discussing evidence for logarithmic behaviour in more general classes of gravity theories including those with boundaries, supersymmetry and galilean relativity. Gurarie has written an historical overview of his seminal contributions to this field, putting his results (and those of his collaborators) in the context of understanding applications to condensed matter physics. This includes the link between the non-diagonalisability of L0 and logarithmic singularities, a study of the c → 0 catastrophe, and a proposed resolution involving supersymmetric partners for the stress-energy tensor and its logarithmic partner field. Henkel and Rouhani describe a direction in which logarithmic singularities are observed in correlators of non-relativistic field theories. Their review covers the appropriate modifications of conformal invariance that are appropriate to non-equilibrium statistical mechanics, strongly anisotropic critical points and certain variants of TMG. The main variation away from the standard relativistic idea of conformal invariance is that time is explicitly distinguished from space when considering dilations and this leads to a variety of algebraic structures to explore. In this review, the link between non-diagonalisable representations and logarithmic singularities in correlators is generalised to these algebras, before two applications of the theory are discussed. Huang and Lepowsky give a non-technical overview of their work on braided tensor structures on suitable categories of representations of vertex operator algebras. They also place their work in historic context and compare it to related approaches. The authors sketch their construction of the so-called P(z)-tensor product of modules of a vertex operator algebra, and the construction of the associativity isomorphisms for this tensor product. They proceed to give a guide to their works leading to the first authorrsquo;s proof of modularity for a class of vertex operator algebras, and to their works, joint with Zhang, on logarithmic intertwining operators and the resulting tensor product theory. Morin-Duchesne and Saint-Aubin have contributed a research article describing their recent characterisation of when the transfer matrix of a periodic loop model fails to be diagonalisable. This generalises their recent result for non-periodic loop models and provides rigorous methods to justify what has often been assumed in the lattice approach to logarithmic CFT. The philosophy here is one of analysing lattice models with finite size, aiming to demonstrate that non-diagonalisability survives the scaling limit. This is extremely difficult in general (see also the review by Gainutdinov et al ), so it is remarkable that it is even possible to demonstrate this at any level of generality. Quella and Schomerus have prepared an extensive review covering their longstanding collaboration on the logarithmic nature of conformal sigma models on Lie supergroups and their cosets with applications to string theory and AdS/CFT. Beginning with a very welcome overview of Lie superalgebras and their representations, harmonic analysis and cohomological reduction, they then apply these mathematical tools to WZW models on type I Lie supergroups and their homogeneous subspaces. Along the way, deformations are discussed and potential dualities in the corresponding string theories are described. Ruelle provides an exhaustive account of his substantial contributions to the study of the abelian sandpile model. This is a statistical model which has the surprising feature that many correlation functions can be computed exactly, in the bulk and on the boundary, even though the spectrum of conformal weights is largely unknown. Nevertheless, there is much evidence suggesting that its scaling limit is described by an, as yet unknown, c = -2 logarithmic CFT. Semikhatov and Tipunin present their very recent results regarding the construction of logarithmic chiral W-algebra extensions of a fractional level algebra. The idea is that these algebras are the centralisers of a rank-two Nichols algebra which possesses at least one fermionic generator. In turn, these Nichols algebra generators are represented by screening operators which naturally appear in CFT bosonisation. The major advantage of using these generators is that they give strong hints about the representation theory and fusion rules of the chiral algebra. Simmons has contributed an article describing the calculation of various correlation functions in the logarithmic CFT that describes critical percolation. These calculations are interpreted geometrically in a manner that should be familiar to mathematicians studying Schramm-Loewner evolutions and point towards a (largely unexplored) bridge connecting logarithmic CFT with this branch of mathematics. Of course, the field of logarithmic CFT has benefited greatly from the work of many of researchers who are not represented in this special issue. The interested reader will find many links to their work in the bibliographies of the special issue articles and reviews. In summary, logarithmic CFT describes an extension of the incredibly successful methods of rational CFT to a more general setting. This extension is necessary to properly describe many different fundamental phenomena of physical interest. The formalism is moreover highly non-trivial from a mathematical point of view and so logarithmic theories are of significant interest to both physicists and mathematicians. We hope that the collection of articles that follows will serve as an inspiration, and a valuable resource, for both of these communities.
Altimetric lagrangian advection to reconstruct Pacific Ocean fine scale surface tracer fields
NASA Astrophysics Data System (ADS)
Rogé, Marine; Morrow, Rosemary; Dencausse, Guillaume
2015-04-01
In past studies, lagrangian stirring of surface tracer fields by altimetric surface geostrophic currents has been performed in different mid to high-latitude regions, showing good results in reconstructing finer-scale tracer patterns. Here we apply the technique to three different regions in the eastern and western tropical Pacific, and in the subtropical southwest Pacific. Initial conditions are derived from weekly gridded temperature and salinity fields, based on hydrographic data and Argo. Validation of the improved fine-scale surface tracer fields is performed using satellite AMSRE SST data, and high-resolution ship thermosalinograph data. We test two kinds of lagrangian advection. The standard one-way advection is shown to introduce an increased tracer bias as the advection time increases. Indeed, since we only use passive stirring, a bias is introduced from the missing physics, such as air-sea fluxes or mixing. A second "backward-forward" advection technique is shown to reduce the seasonal bias, but more data is lost around coasts and islands, a strong handicap in the tropical Pacific with many small islands. In the subtropical Pacific Ocean, the mesoscale temperature and salinity fronts are well represented by the one-way advection over a 10-day advection time, including westward propagating features not apparent in the initial fields. In the tropics, the results are less clear. The validation is hampered by the complex vertical stratification, and the technique is limited by the lack of accurate surface currents for the stirring - the gridded altimetric fields poorly represent the meridional currents, and are not detecting the fast tropical instability waves, nor the wind-driven circulation. We suggest that the passive lateral stirring technique is efficient in regions with moderate the high mesoscale energy and correlated mesoscale surface temperature and surface height. In other regions, more complex dynamical processes may need to be included.
Polymer parametrized field theory
Laddha, Alok; Varadarajan, Madhavan
2008-08-15
Free scalar field theory on 2-dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using loop quantum gravity (LQG) type 'polymer' representations for the matter field and the inertial variables. The quantum constraints are solved via group averaging techniques and, analogous to the case of spatial geometry in LQG, the smooth (flat) spacetime geometry is replaced by a discrete quantum structure. An overcomplete set of Dirac observables, consisting of (a) (exponentials of) the standard free scalar field creation-annihilation modes and (b) canonical transformations corresponding to conformal isometries, are represented as operators on the physical Hilbert space. None of these constructions suffer from any of the 'triangulation'-dependent choices which arise in treatments of LQG. In contrast to the standard Fock quantization, the non-Fock nature of the representation ensures that the group of conformal isometries as well as that of the gauge transformations generated by the constraints are represented in an anomaly free manner. Semiclassical states can be analyzed at the gauge invariant level. It is shown that 'physical weaves' necessarily underlie such states and that such states display semiclassicality with respect to, at most, a countable subset of the (uncountably large) set of observables of type (a). The model thus offers a fertile testing ground for proposed definitions of quantum dynamics as well as semiclassical states in LQG.
Lagrangian model for the evolution of turbulent magnetic and passive scalar fields
Hater, T.; Grauer, R.; Homann, H.
2011-01-15
In this Brief Report we present an extension of the recent fluid deformation (RFD) closure introduced by Chevillard and Meneveau [L. Chevillard and C. Meneveau, Phys. Rev. Lett. 97, 174501 (2006)] which was developed for modeling the time evolution of Lagrangian fluctuations in incompressible Navier-Stokes turbulence. We apply the RFD closure to study the evolution of magnetic and passive scalar fluctuations. This comparison is especially interesting since the stretching term for the magnetic field and for the gradient of the passive scalar are similar but differ by a sign such that the effect of stretching and compression by the turbulent velocity field is reversed. Probability density functions (PDFs) of magnetic fluctuations and fluctuations of the gradient of the passive scalar obtained from the RFD closure are compared against PDFs obtained from direct numerical simulations.
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields. PMID:25763950
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Scalar field theory on noncommutative Snyder spacetime
Battisti, Marco Valerio; Meljanac, Stjepan
2010-07-15
We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincare group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.
A Lagrangian description of nearshore hydrodynamics and rip currents forced by a random wave field
NASA Astrophysics Data System (ADS)
Leandro, S.; Cienfuegos, R.; Escauriaza, C. R.
2011-12-01
Nonlinear processes become important for waves propagating in the shoaling and surf zones. Wave shape changes when approaching the coast under the influence of bathymetry, becoming increasingly asymmetric until reaching the breaking limit. In the shoaling zone, non-linearities induce a net velocity in the direction of wave propagation, a phenomenon called Stokes drift, while in the surf zone, currents are mainly driven by spatio-temporal variations in energy dissipation gradients. In this work we aim at investigating and characterizing the nearshore circulation forced by a random wave field propagating over a variable bathymetry. We carry out numerical simulations over a laboratory experiment conducted in a wave basin over a realistic bathymetry [Michallet et al. 2010]. For the hydrodynamics, we use a 2D shock-capturing finite-volume model that solves the non-linear shallow water equations, taking into account energy dissipation by breaking, friction, bed-slope variations, and an accurate description for the moving shoreline in the swash zone [Marche et al. 2007;Guerra et al. 2010]. Model predictions are compared and validated against experimental data giving confidence for its use in the description of wave propagation in the surf/swash zone, together with mean eulerian velocities. The resulting wave propagation and circulation provided by the 2D model will then be used to describe drifter's patterns in the surf zone and construct Lagrangian particle tracking. The chosen experimental configuration is of great interest due to the random wave forcing (slowly modulated), the beach non-uniformities, and the existence of several bar-rip channels that enhance quasi-periodic rip instabilities. During the experiment, balloons filled with water, with a diameter between 5 and 10 cm, were placed in the surf zone in order to characterize circulation in a Lagrangian framework [Castelle et al. 2010]. The time-location of the balloons was continuously tracked by a shore-mounted video camera, and the images were processed to obtain the trajectories and mean velocities. The Lagrangian description provided by the numerical model will be thus confronted to experimental data, and then used to characterize circulation patterns, rip instabilities and infragravity wave pulsations.
Field theory and particle physics
Eboli, O.J.P.; Gomes, M.; Santoro, A.
1990-01-01
This book contains the proceedings of the topics covered during the fifth Jorge Andre Swieca Summer School. The first part of the book collects the material devoted to quantum field theory. There were four courses on methods in Field Theory; H. O. Girotti lectured on constrained dynamics, R. Jackiw on the Schrodinger representation in Field Theory, S.-Y. Pi on the application of this representation to quantum fields in a Robertson-Walker spacetime, and L. Vinet on Berry Connections. There were three courses on Conformal Field Theory: I. Todorov focused on the problem of construction and classification of conformal field theories. Lattice models, two-dimensional S matrices and conformal field theory were looked from the unifying perspective of the Yang-Baxter algebras in the lectures given by M. Karowski. Parasupersymmetric quantum mechanics was discussed in the lectures by L. Vinet. Besides those courses, there was an introduction to string field theory given by G. Horowitz. There were also three seminars: F. Schaposnik reported on recent applications of topological methods in field theory, P. Gerbert gave a seminar on three dimensional gravity and V. Kurak talked on two dimensional parafermionic models. The second part of this proceedings is devoted to phenomenology. There were three courses on Particle Physics: Dan Green lectured on collider physics, E. Predrazzi on strong interactions and G. Cohen-Tanoudji on the use of strings in strong interactions.
NASA Astrophysics Data System (ADS)
Weinberg, Steven
1995-06-01
In The Quantum Theory of Fields, Nobel Laureate Steven Weinberg combines his exceptional physical insight with his gift for clear exposition to provide a self-contained, comprehensive, and up-to-date introduction to quantum field theory. This is a two-volume work. Volume I introduces the foundations of quantum field theory. The development is fresh and logical throughout, with each step carefully motivated by what has gone before, and emphasizing the reasons why such a theory should describe nature. After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and the properties of particles that follow from these principles. Quantum field theory emerges from this as a natural consequence. The author presents the classic calculations of quantum electrodynamics in a thoroughly modern way, showing the use of path integrals and dimensional regularization. His account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum electrodynamics to elementary particle physics, and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. This work will be an invaluable reference for all physicists and mathematicians who use quantum field theory, and it is also appropriate as a textbook for graduate students in this area.
Invariants from classical field theory
Diaz, Rafael; Leal, Lorenzo
2008-06-15
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.
Two-way Interaction of Lagrangian Bubble Dynamics and Eulerian Mixture Flow Field
NASA Astrophysics Data System (ADS)
Choi, Jin-Keun; Hsiao, Chao-Tsung; Chahine, Georges
2007-11-01
Although under simple flow conditions a well dispersed bubble cloud in a liquid can be modeled with an Eulerian continuum model, the fine scale interactions between the two phases, the potential non-uniformities and high bubble concentrations in stiff gradient regions of complex flows can only be represented by more detailed numerical models such as Lagrangian tracking of individual bubbles. To meet both needs of describing individual bubbles and of including the collective effects in the two-phase continuum, we have developed a method coupling in a two-way fashion the two approaches. The bubble dynamics and tracking scheme is based on extensive studies on bubble dynamics and interactions at Dynaflow and is based on a Surface Averaged Pressure spherical model using a modified incompressible Rayleigh-Plesset equation or a modified compressible Gilmore equation. The bubbles presence in the Eulerian flow field is considered through a variable medium density formulation resulting from the instantaneous bubble population distribution in the field. The developed method is applicable to many practical flows in pipes, jets, pumps, propellers, ships, and the ocean. We present the method and its application to waterjet thrust augmentation by bubble injection.
Reparametrizations and Gauge and General Coordinate Transformations in String Field Theory
Das, Sumit R.; Rubin, Mark A.
1985-10-01
The authors relate reparametrizations of the parameter σ to point transformations of scalar field in ''loop space,'' the configuration space of string field theory. Formulas are given for the changes induced by these transformations in the infinite set of ''component'' spacetime-tensor fields into which a scalar field on loop space may be decomposed. New derivative operators on loop space are defined, motivated by the parametrization-dependence of the mapping from loop space to spacetime. A generalization to loop space of the Einstein-Hilbert Lagrangian is proposed as a candidate for a 2nd-quantized string Lagrangian not tied to any preferred background geometry.
NASA Astrophysics Data System (ADS)
Gleicher, S.; Chamecki, M.; Isard, S.; Katul, G. G.
2012-12-01
Plant disease epidemics caused by pathogenic spores are a common and consequential threat to agricultural crops. In most cases, pathogenic spores are produced and released deep inside plant canopies and must be transported out of the canopy region in order to infect other fields and spread the disease. The fraction of spores that "escape" the canopy is crucial in determining how fast and far these plant diseases will spread. The goal of this work is to use a field experiment, coupled with a Lagrangian Stochastic Model (LSM), to investigate how properties of canopy turbulence impact the dispersion of spores inside the canopy and the fraction of spores that escape from the canopy. An extensive field experiment was conducted to study spore dispersion inside and outside a corn canopy. The spores were released from point sources located at various depths inside the canopy. Concentration measurements were obtained inside and above the canopy by a 3-dimensional grid of spore collectors. The experimental measurements of mean spore concentration are used to validate a LSM for spore dispersion. In the LSM, flow field statistics used to drive the particle dispersion are specified by a second-order closure model for turbulence within plant canopies. The dispersion model includes spore deposition on and rebound from canopy elements. The combination of experimental and numerical simulations is used to quantify the fraction of spores that escape the canopy. Effects of release height, friction velocity, and canopy architecture on the escape fraction of spores are explored using the LSM, and implications for disease propagation are discussed.
Pasti, Paolo; Tonin, Mario; Samsonov, Igor; Sorokin, Dmitri
2009-10-15
We reveal nonmanifest gauge and SO(1,5) Lorentz symmetries in the Lagrangian description of a six-dimensional free chiral field derived from the Bagger-Lambert-Gustavsson model in [P.-M. Ho and Y. Matsuo, J. High Energy Phys. 06 (2008) 105.] and make this formulation covariant with the use of a triplet of auxiliary scalar fields. We consider the coupling of this self-dual construction to gravity and its supersymmetrization. In the case of the nonlinear model of [P.-M. Ho, Y. Imamura, Y. Matsuo, and S. Shiba, J. High Energy Phys. 08 (2008) 014.] we solve the equations of motion of the gauge field, prove that its nonlinear field strength is self-dual and find a gauge-covariant form of the nonlinear action. Issues of the relation of this model to the known formulations of the M5-brane worldvolume theory are discussed.
Finite-Temperature Field Theory
NASA Astrophysics Data System (ADS)
Kapusta, Joseph I.
1994-01-01
Professor Kapusta develops the basic formalism and theoretical techniques for studying relativistic quantum field theory at high temperature and density. Topics covered include functional integral representation of the partition function, diagrammatic expansions, linear response theory, screening and collective oscillations, equations of state, phase transitions, restoration of spontaneously broken symmetries, the Goldstone theorem, and infrared problems. Specific physical theories treated include QED, QCD, the Weinberg-Salam model, and effective nuclear field theories. Applications to white dwarfs, neutron stars, ultrarelativistic nucleus-nucleus collisions, and the early universe are discussed. Problems are provided at the end of each chapter, and numerous references to the literature are included.
A new bound constraints method for 3-D potential field data inversion using Lagrangian multipliers
NASA Astrophysics Data System (ADS)
Zhang, Yi; Yan, Jianguo; Li, Fei; Chen, Chao; Mei, Bao; Jin, Shuanggen; Dohm, James H.
2015-04-01
In this paper, we present a method for incorporating prior geological information into potential field data inversion problem. As opposed to the traditional inverse algorithm, our proposed method takes full advantage of prior geological information as a constraint and thus obtains a new objective function for inversion by adding Lagrangian multipliers and slack variables to the traditional inversion method. These additional parameters can be easily solved during iterations. We used both synthetic and observed data sets to test the stability and validity of the proposed method. Our results using synthetic gravity data show that our new method predicts depth and density anomalies more efficiently and accurately than the traditional inversion method that does not include prior geological constraints. Then using observed gravity data in the Three Gorges area and geological constraint information, we obtained the density distribution of the upper and middle crust in this area thus revealing its geological structure. These results confirm the proposed method's validity and indicate its potential application for magnetism data inversion and exploration of geological structures.
The $\\hbar$ Expansion in Quantum Field Theory
Brodsky, Stanley J.; Hoyer, Paul
2010-10-27
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
Theory of fossil magnetic field
NASA Astrophysics Data System (ADS)
Dudorov, Alexander E.; Khaibrakhmanov, Sergey A.
2015-02-01
Theory of fossil magnetic field is based on the observations, analytical estimations and numerical simulations of magnetic flux evolution during star formation in the magnetized cores of molecular clouds. Basic goals, main features of the theory and manifestations of MHD effects in young stellar objects are discussed.
Families of Particles with Different Masses in PT-Symmetric Quantum Field Theory
Bender, Carl M.; Klevansky, S. P.
2010-07-16
An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when the functional integral for the Green's functions of the quantum field theory converges in different pairs of Stokes' wedges in complex-field space, and the solutions are physically viable if the pairs of Stokes' wedges are PT symmetric.
Einstein-aether theory with a Maxwell field: General formalism
Balakin, Alexander B.; Lemos, José P.S.
2014-11-15
We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.
Double field theory inspired cosmology
Wu, Houwen; Yang, Haitang E-mail: hyanga@scu.edu.cn
2014-07-01
Double field theory proposes a generalized spacetime action possessing manifest T-duality on the level of component fields. We calculate the cosmological solutions of double field theory with vanishing Kalb-Ramond field. It turns out that double field theory provides a more consistent way to construct cosmological solutions than the standard string cosmology. We construct solutions for vanishing and non-vanishing symmetry preserving dilaton potentials. The solutions assemble the pre- and post-big bang evolutions in one single line element. Our results show a smooth evolution from an anisotropic early stage to an isotropic phase without any special initial conditions in contrast to previous models. In addition, we demonstrate that the contraction of the dual space automatically leads to both an inflation phase and a decelerated expansion of the ordinary space during different evolution stages.
On the Lagrangian description of unsteady boundary-layer separation. I - General theory
NASA Technical Reports Server (NTRS)
Van Dommelen, Leon L.; Cowley, Stephen J.
1990-01-01
Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.
On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory
NASA Technical Reports Server (NTRS)
Vandommelen, Leon L.; Cowley, Stephen J.
1989-01-01
Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.
Böckmann, Marcus; Doltsinis, Nikos L; Marx, Dominik
2015-06-01
An extended Lagrangian formalism that allows for a smooth transition between two different descriptions of interactions during a molecular dynamics simulation is presented. This time-adaptive method is particularly useful in the context of multiscale simulation as it provides a sound recipe to switch on demand between different hierarchical levels of theory, for instance between ab initio ("QM") and force field ("MM") descriptions of a given (sub)system in the course of a molecular dynamics simulation. The equations of motion can be integrated straightforwardly using the usual propagators, such as the Verlet algorithm. First test cases include a bath of harmonic oscillators, of which a subset is switched to a different force constant and/or equilibrium position, as well as an all-MM to QM/MM transition in a hydrogen-bonded water dimer. The method is then applied to a smectic 8AB8 liquid crystal and is shown to be able to switch dynamically a preselected 8AB8 molecule from an all-MM to a QM/MM description which involves partition boundaries through covalent bonds. These examples show that the extended Lagrangian approach is not only easy to implement into existing code but that it is also efficient and robust. The technique moreover provides easy access to a conserved energy quantity, also in cases when Nosé-Hoover chain thermostatting is used throughout dynamical switching. A simple quadratic driving potential proves to be sufficient to guarantee a smooth transition whose time scale can be easily tuned by varying the fictitious mass parameter associated with the auxiliary variable used to extend the Lagrangian. The method is general and can be applied to time-adaptive switching on demand between two different levels of theory within the framework of hybrid scale-bridging simulations. PMID:26575543
Geometer energy unified field theory
NASA Astrophysics Data System (ADS)
Rivera, Susana; Rivera, Anacleto
GEOMETER - ENERGY UNIFIED FIELD THEORY Author: Anacleto Rivera Nivón Co-author: Susana Rivera Cabrera This work is an attempt to find the relationship between the Electromagnetic Field and the Gravitational Field. Despite it is based on the existence of Strings of Energy, it is not the same kind of strings that appears on other theories like Superstring Theory, Branas Theory, M - Theory, or any other related string theories. Here, the Strings are concentrated energy lines that vibrates, and experiences shrinking and elongations, absorbing and yielding on each contraction and expansion all that is found in the Universe: matter and antimatter, waves and energy in all manifestations. In contrast to superstring theory, which strings are on the range of the Length of Planck, these Strings can be on the cosmological size, and can contain many galaxies, or clusters, or groups of galaxies; but also they can reach as small sizes as subatomic levels. Besides, and contrary to what it is stated in some other string theories that need the existence of ten or more dimensions, the present proposal sustains in only four particular dimensions. It has been developed a mathematical support that will try to help to improve the understanding of the phenomena that take place at the Universe.
Loops in exceptional field theory
NASA Astrophysics Data System (ADS)
Bossard, Guillaume; Kleinschmidt, Axel
2016-01-01
We study certain four-graviton amplitudes in exceptional field theory in dimensions D ≥ 4 up to two loops. As the formulation is manifestly invariant under the U-duality group {E}_{11-D}({Z}) , our resulting expressions can be expressed in terms of automorphic forms. In the low energy expansion, we find terms in the M-theory effective action of type R 4, ∇4 R 4 and ∇6 R 4 with automorphic coefficient functions in agreement with independent derivations from string theory. This provides in particular an explicit integral formula for the exact string theory ∇6 R 4 threshold function. We exhibit moreover that the usual supergravity logarithmic divergences cancel out in the full exceptional field theory amplitude, within an appropriately defined dimensional regularisation scheme. We also comment on terms of higher derivative order and the role of the section constraint for possible counterterms.
Finite-temperature field theory.
NASA Astrophysics Data System (ADS)
Kapusta, J. I.
This book develops the basic formalism and theoretical techniques for studying relativistic quantum field theory at high temperature and density. Topics include functional integral representation of the partition function, diagrammatic expansions, linear response theory, screening and collective oscillations, equations of state, phase transitions, restoration of spontaneously broken symmetries, Goldstone theorem, and infrared problems. Specific physical theories treated include QED, QCD, the Weinberg-Salam model, and effective nuclear field theories. Applications to white dwarf stars, neutron stars, ultrarelativistic nucleus-nucleus collisions, and the early universe are discussed. Contents: 1. Review of quantum statistical mechanics. 2. Functional integral representation of the partition function. 3. Interactions and diagrammatic techniques. 4. Renormalization. 5. Quantum electrodynamics. 6. Linear response theory. 7. Spontaneous symmetry breaking and restoration. 8. Quantum chromodynamics. 9. Weak interactions. 10. Nuclear matter. Conclusion.
Boundary Integrable Quantum Field Theories
NASA Astrophysics Data System (ADS)
Dorey, Patrick
2001-04-01
These lectures concerned the properties of quantum field theories in the presence of boundaries. There are many different approaches to this subject. One can begin by studying conformal field theories with boundaries - the principal theme of the lectures at this school by Jean-Bernard Zuber and by Christoph Schweigert - and then, as described in Gérard Watts' lectures, consider their perturbations. In many cases these perturbations result in massive integrable quantum field theories, and it was the direct study of such theories in their own right that formed my main topic. A number of reviews of this subject can be found on the electronic archives, and so in this contribution I shall restrict myself to an outline of the questions touched on in my talks, and a brief list of references to which the interested reader can turn to find at least some of the answers...
(Studies in quantum field theory)
Not Available
1990-01-01
During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity.
Lagrangian description of warm plasmas
NASA Technical Reports Server (NTRS)
Kim, H.
1970-01-01
Efforts are described to extend the averaged Lagrangian method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the expanded microscopic Lagrangian. As applications of the microscopic Lagrangian, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.
NASA Astrophysics Data System (ADS)
Evans, M. J.; Shallcross, D. E.; Law, K. S.; Wild, J. O. F.; Simmonds, P. G.; Spain, T. G.; Berrisford, P.; Methven, J.; Lewis, A. C.; McQuaid, J. B.; Pilling, M. J.; Bandy, B. J.; Penkett, S. A.; Pyle, J. A.
The Cambridge Tropospheric Trajectory model of Chemistry and Transport (CiTTyCAT), a Lagrangian chemistry model, has been evaluated using atmospheric chemical measurements collected during the East Atlantic Summer Experiment 1996 (EASE '96). This field campaign was part of the UK Natural Environment Research Council's (NERC) Atmospheric Chemistry Studies in the Oceanic Environment (ACSOE) programme, conducted at Mace Head, Republic of Ireland, during July and August 1996. The model includes a description of gas-phase tropospheric chemistry, and simple parameterisations for surface deposition, mixing from the free troposphere and emissions. The model generally compares well with the measurements and is used to study the production and loss of O 3 under a variety of conditions. The mean difference between the hourly O 3 concentrations calculated by the model and those measured is 0.6 ppbv with a standard deviation of 8.7 ppbv. Three specific air-flow regimes were identified during the campaign - westerly, anticyclonic (easterly) and south westerly. The westerly flow is typical of background conditions for Mace Head. However, on some occasions there was evidence of long-range transport of pollutants from North America. In periods of anticyclonic flow, air parcels had collected emissions of NO x and VOCs immediately before arriving at Mace Head, leading to O 3 production. The level of calculated O 3 depends critically on the precise details of the trajectory, and hence on the emissions into the air parcel. In several periods of south westerly flow, low concentrations of O 3 were measured which were consistent with deposition and photochemical destruction inside the tropical marine boundary layer.
NASA Astrophysics Data System (ADS)
Barutello, Vivina; Jadanza, Riccardo D.; Portaluri, Alessandro
2016-01-01
It is well known that the linear stability of the Lagrangian elliptic solutions in the classical planar three-body problem depends on a mass parameter β and on the eccentricity e of the orbit. We consider only the circular case ( e = 0) but under the action of a broader family of singular potentials: α-homogeneous potentials, for α in (0, 2), and the logarithmic one. It turns out indeed that the Lagrangian circular orbit persists also in this more general setting. We discover a region of linear stability expressed in terms of the homogeneity parameter α and the mass parameter β, then we compute the Morse index of this orbit and of its iterates and we find that the boundary of the stability region is the envelope of a family of curves on which the Morse indices of the iterates jump. In order to conduct our analysis we rely on a Maslov-type index theory devised and developed by Y. Long, X. Hu and S. Sun; a key role is played by an appropriate index theorem and by some precise computations of suitable Maslov-type indices.
A view on coupled cluster perturbation theory using a bivariational Lagrangian formulation.
Kristensen, Kasper; Eriksen, Janus J; Matthews, Devin A; Olsen, Jeppe; Jørgensen, Poul
2016-02-14
We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the Møller-Plesset fluctuation potential. We initially introduce the E-CCSD(T-n) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T-n) series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. The computational scaling is similar for the two series, and both are term-wise size extensive with a formal convergence towards the CCSDT target energy. However, the two series are different, and the CCSD(T-n) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the E-CCSD(T-n) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higher-level target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC Lagrangian (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a different and faster convergent perturbation series than the simpler energy-based expansion. PMID:26874478
A view on coupled cluster perturbation theory using a bivariational Lagrangian formulation
NASA Astrophysics Data System (ADS)
Kristensen, Kasper; Eriksen, Janus J.; Matthews, Devin A.; Olsen, Jeppe; Jørgensen, Poul
2016-02-01
We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the Møller-Plesset fluctuation potential. We initially introduce the E-CCSD(T-n) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T-n) series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. The computational scaling is similar for the two series, and both are term-wise size extensive with a formal convergence towards the CCSDT target energy. However, the two series are different, and the CCSD(T-n) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the E-CCSD(T-n) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higher-level target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC Lagrangian (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a different and faster convergent perturbation series than the simpler energy-based expansion.
Souvatzis, Petros; Niklasson, Anders M. N.
2013-12-07
We present an efficient general approach to first principles molecular dynamics simulations based on extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] in the limit of vanishing self-consistent field optimization. The reduction of the optimization requirement reduces the computational cost to a minimum, but without causing any significant loss of accuracy or long-term energy drift. The optimization-free first principles molecular dynamics requires only one single diagonalization per time step, but is still able to provide trajectories at the same level of accuracy as exact, fully converged, Born-Oppenheimer molecular dynamics simulations. The optimization-free limit of extended Lagrangian Born-Oppenheimer molecular dynamics therefore represents an ideal starting point for robust and efficient first principles quantum mechanical molecular dynamics simulations.
Exceptional field theory: SL(5)
NASA Astrophysics Data System (ADS)
Musaev, Edvard T.
2016-02-01
In this work the exceptional field theory formulation of supergravity with SL (5) gauge group is considered. This group appears as a U-duality group of D = 7 maximal supergravity. In the formalism presented the hidden global duality group is promoted into a gauge group of a theory in dimensions 7+number of extended directions. This work is a continuation of the series of works for E 8,7,6 , SO (5 , 5) and SL (3) × SL (2) duality groups.
NASA Technical Reports Server (NTRS)
Broucke, R.; Lass, H.
1975-01-01
It is shown that it is possible to make a change of variables in a Lagrangian in such a way that the number of variables is increased. The Euler-Lagrange equations in the redundant variables are obtained in the standard way (without the use of Lagrange multipliers). These equations are not independent but they are all valid and consistent. In some cases they are simpler than if the minimum number of variables are used. The redundant variables are supposed to be related to each other by several constraints (not necessarily holonomic), but these constraints are not used in the derivation of the equations of motion. The method is illustrated with the well known Kustaanheimo-Stiefel regularization. Some interesting applications to perturbation theory are also described.
Quantum Field Theory in Condensed Matter Physics
NASA Astrophysics Data System (ADS)
Tsvelik, Alexei M.
2007-01-01
Preface; Acknowledgements; Part I. Introduction to Methods: 1. QFT: language and goals; 2. Connection between quantum and classical: path integrals; 3. Definitions of correlation functions: Wick's theorem; 4. Free bosonic field in an external field; 5. Perturbation theory: Feynman diagrams; 6. Calculation methods for diagram series: divergences and their elimination; 7. Renormalization group procedures; 8. O(N)-symmetric vector model below the transition point; 9. Nonlinear sigma models in two dimensions: renormalization group and 1/N-expansion; 10. O(3) nonlinear sigma model in the strong coupling limit; Part II. Fermions: 11. Path integral and Wick's theorem for fermions; 12. Interaction electrons: the Fermi liquid; 13. Electrodynamics in metals; 14. Relativistic fermions: aspects of quantum electrodynamics; 15. Aharonov-Bohm effect and transmutation of statistics; Part III. Strongly Fluctuating Spin Systems: Introduction; 16. Schwinger-Wigner quantization procedure: nonlinear sigma models; 17. O(3) nonlinear sigma model in (2+1) dimensions: the phase diagram; 18. Order from disorder; 19. Jordan-Wigner transformations for spin S=1/2 models in D=1, 2, 3; 20. Majorana representation for spin S=1/2 magnets: relationship to Z2 lattice gauge theories; 21. Path integral representations for a doped antiferromagnet; Part IV. Physics in the World of One Spatial Dimension: Introduction; 22. Model of the free bosonic massless scalar field; 23. Relevant and irrelevant fields; 24. Kosterlitz-Thouless transition; 25. Conformal symmetry; 26. Virasoro algebra; 27. Differential equations for the correlation functions; 28. Ising model; 29. One-dimensional spinless fermions: Tomonaga-Luttinger liquid; 30. One-dimensional fermions with spin: spin-charge separation; 31. Kac-Moody algebras: Wess-Zumino-Novikov-Witten model; 32. Wess-Zumino-Novikov-Witten model in the Lagrangian form: non-Abelian bosonization; 33. Semiclassical approach to Wess-Zumino-Novikov-Witten models; 34. Integrable models: dynamical mass generation; 35. A comparative study of dynamical mass generation in one and three dimensions; 36. One-dimensional spin liquids: spin ladder and spin S=1 Heisenberg chain; 37. Kondo chain; 38. Gauge fixing in non-Abelian theories: (1+1)-dimensional quantum chromodynamics; Select bibliography; Index.
Introduction to string theory and conformal field theory
Belavin, A. A. Tarnopolsky, G. M.
2010-05-15
A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.
NASA Astrophysics Data System (ADS)
Sanchez, Raul; Newman, David
2014-10-01
Turbulent velocity fields can generate perturbations of the electric current and magnetic field that, under certain conditions, may generate an average, large-scale magnetic field. Such generation is important to understand the behavior of stars, planetary and laboratory plasmas. This generation is traditionally studied by assuming near-Gaussian, random velocity fluctuations. This simplification allows to exprese the effective electromotive force in Faraday's law in terms of a piece proportional to the large-scale magnetic field itself (the α-term) and another proportional to its curl (the β term) assuming certain symmetry conditions are met. Physically, the α-term is a measure of the mean helicity of the flow and drives the dynamo process. In a previous contribution, we examined theoretically what consequences would follow from assuming instead Levy-distributed, Lagrangianly-correlated velocity fields, that have been recently identified as of relevance in regimes of near-marginal turbulence or in the presence of a strong, stable sheared flow. Here, we will discuss and extend these results numerically by implementing the kinematic dynamo equation using a Lagrangian, meshless numerical method inspired by the SPH schemes frequently used in hydrodynamics.
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2004-08-27
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end. PMID:15447078
Planar limit of orientifold field theories and emergent center symmetry
Armoni, Adi; Shifman, Mikhail; Uensal, Mithat
2008-02-15
We consider orientifold field theories [i.e., SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations] on R{sub 3}xS{sub 1} where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills theory. The latter has Z{sub N} center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from Z{sub N} symmetric to Z{sub N} broken phase applies. At the Lagrangian level the orientifold theories have at most a Z{sub 2} center. We discuss how the full Z{sub N} center symmetry dynamically emerges in the orientifold theories in the limit N{yields}{infinity}. In the confining phase the manifestation of this enhancement is the existence of stable k strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.
Bias in the effective field theory of large scale structures
NASA Astrophysics Data System (ADS)
Senatore, Leonardo
2015-11-01
We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what was recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local in space, but non-local in time, and we explain the observational consequences of this fact. We give an argument for why to a certain degree of accuracy the theory can be considered as quasi time-local and explain what the operator structure is in this case. We describe renormalization of the bias coefficients so that, after this and after upgrading the Eulerian calculation to a Lagrangian one, the perturbative series for galaxies correlation functions results in a manifestly convergent expansion in powers of k/kNL and k/kM, where k is the wavenumber of interest, kNL is the wavenumber associated to the non-linear scale, and kM is the comoving wavenumber enclosing the mass of a galaxy.
Density Functional Theory from Effective Field Theory
NASA Astrophysics Data System (ADS)
Furnstahl, Richard
2006-04-01
The combination of progress in chiral effective field theory (EFT) for inter-nucleon interactions, the application of renormalization group (RG) techniques to nuclear systems, and advances in many-body computational tools and methods opens the possibility of constructive density functional theory (DFT) for nuclei. Effective actions provide a natural framework for the development of EFT/DFT. One approach uses EFT power counting to define an order-by-order inversion of the generating functional in the presence of a source coupled to the density. This leads directly to Kohn-Sham DFT, which is widely used in condensed matter and quantum chemistry applications. Natural extensions lead to functionals of more general densities and the incorporation of pairing, consistent with phenomenological energy functionals for nuclei, which are themselves consistent with chiral EFT power counting. Chiral EFT offers a model-independent starting point, including a systematic approach to many-nucleon forces. The chiral inter-nucleon interactions are constructed with cutoffs in relative momentum much lower than those in conventional potentials, resulting in much softer interactions. If RG techniques are used to lower the cutoff further while preserving observables, Hartree-Fock plus second-order contributions (with three-body forces included) is found to be a good, possibly perturbative, first approximation for nuclear matter. The dominance of Hartree-Fock, in common with Coulomb DFT, raises hope for a quantitative microscopic construction. There are significant challenges to realizing this goal, both conceptual and technical, such as arise in extending DFT to self-bound systems. But the path is reasonably clear and meshes well with on-going efforts to develop, refine, and test phenomenological energy functionals for application across the mass table.
A multisymplectic approach to defects in integrable classical field theory
NASA Astrophysics Data System (ADS)
Caudrelier, V.; Kundu, A.
2015-02-01
We introduce the concept of multisymplectic formalism, familiar in covariant field theory, for the study of integrable defects in 1 + 1 classical field theory. The main idea is the coexistence of two Poisson brackets, one for each spacetime coordinate. The Poisson bracket corresponding to the time coordinate is the usual one describing the time evolution of the system. Taking the nonlinear Schrödinger (NLS) equation as an example, we introduce the new bracket associated to the space coordinate. We show that, in the absence of any defect, the two brackets yield completely equivalent Hamiltonian descriptions of the model. However, in the presence of a defect described by a frozen Bäcklund transformation, the advantage of using the new bracket becomes evident. It allows us to reinterpret the defect conditions as canonical transformations. As a consequence, we are also able to implement the method of the classical r matrix and to prove Liouville integrability of the system with such a defect. The use of the new Poisson bracket completely bypasses all the known problems associated with the presence of a defect in the discussion of Liouville integrability. A by-product of the approach is the reinterpretation of the defect Lagrangian used in the Lagrangian description of integrable defects as the generating function of the canonical transformation representing the defect conditions.
NASA Astrophysics Data System (ADS)
Oettl, Dietmar
2015-05-01
A revised microscale flow field model has been implemented in the Lagrangian particle model Graz Lagrangian Model (GRAL) for computing flows around obstacles. It is based on the Reynolds-averaged Navier-Stokes equations in three dimensions and the widely used standard turbulence model. Here we focus on evaluating the model regarding computed concentrations by use of a comprehensive wind-tunnel experiment with numerous combinations of building geometries, stack positions, and locations. In addition, two field experiments carried out in Denmark and in the U.S were used to evaluate the model. Further, two different formulations of the standard deviation of wind component fluctuations have also been investigated, but no clear picture could be drawn in this respect. Overall the model is able to capture several of the main features of pollutant dispersion around obstacles, but at least one future model improvement was identified for stack releases within the recirculation zone of buildings. Regulatory applications are the bread-and-butter of most GRAL users nowadays, requiring fast and robust modelling algorithms. Thus, a few simplifications have been introduced to decrease the computational time required. Although predicted concentrations for the two field experiments were found to be in good agreement with observations, shortcomings were identified regarding the extent of computed recirculation zones for the idealized wind-tunnel building geometries, with approaching flows perpendicular to building faces.
Variational methods for field theories
Ben-Menahem, S.
1986-09-01
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
Diffeomorphisms in group field theories
Baratin, Aristide; Girelli, Florian; Oriti, Daniele
2011-05-15
We study the issue of diffeomorphism symmetry in group field theories (GFT), using the noncommutative metric representation introduced by A. Baratin and D. Oriti [Phys. Rev. Lett. 105, 221302 (2010).]. In the colored Boulatov model for 3d gravity, we identify a field (quantum) symmetry which ties together the vertex translation invariance of discrete gravity, the flatness constraint of canonical quantum gravity, and the topological (coarse-graining) identities for the 6j symbols. We also show how, for the GFT graphs dual to manifolds, the invariance of the Feynman amplitudes encodes the discrete residual action of diffeomorphisms in simplicial gravity path integrals. We extend the results to GFT models for higher-dimensional BF theories and discuss various insights that they provide on the GFT formalism itself.
Dynamics of perturbations in Double Field Theory & non-relativistic string theory
NASA Astrophysics Data System (ADS)
Ko, Sung Moon; Melby-Thompson, Charles M.; Meyer, Ren; Park, Jeong-Hyuck
2015-12-01
Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry not only globally (`non-geometry'), but even locally (`non-Riemannian'). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri [1] arises precisely as such a non-Riemannian string background, and that the Gomis-Ooguri sigma model is equivalent to the Double Field Theory sigma model of [2] on this background. We further show that the target-space formulation of Double Field Theory on this non-Riemannian background correctly reproduces the appropriate sector of the Gomis-Ooguri string spectrum. To do this, we develop a general semi-covariant formalism describing perturbations in Double Field Theory. We derive compact expressions for the linearized equations of motion around a generic on-shell background, and construct the corresponding fluctuation Lagrangian in terms of novel completely covariant second order differential operators. We also present a new non-Riemannian solution featuring Schrdinger conformal symmetry.
Hydrodynamic Lagrangian of relativistic superfluids with crystalline structure
NASA Astrophysics Data System (ADS)
Peletminskii, A. S.
2009-09-01
We propose a relativistic Lagrangian formulation of macroscopic dynamics of superfluid systems. The constructed Lagrangian provides the description of ordinary superfluids and superfluids with a crystalline ordering, where both phase and translational symmetries are simultaneously broken (e.g., supersolids or crystalline superfluids in neutron stars). The covariant conservation laws and equations of motion for the field variables associated with the broken symmetries are obtained. The connection to Khalatnikov-Lebedev relativistic hydrodynamic theory is discussed.
Quantum field perturbation theory revisited
NASA Astrophysics Data System (ADS)
Matone, Marco
2016-03-01
Schwinger's formalism in quantum field theory can be easily implemented in the case of scalar theories in D dimension with exponential interactions, such as μDexp (α ϕ ). In particular, we use the relation exp (α δ/δ J (x ) )exp (-Z0[J ])=exp (-Z0[J +αx]) with J the external source, and αx(y )=α δ (y -x ). Such a shift is strictly related to the normal ordering of exp (α ϕ ) and to a scaling relation which follows by renormalizing μ . Next, we derive a new formulation of perturbation theory for the potentials V (ϕ )=λ/n ! :ϕn: , using the generating functional associated to :exp (α ϕ ):. The Δ (0 )-terms related to the normal ordering are absorbed at once. The functional derivatives with respect to J to compute the generating functional are replaced by ordinary derivatives with respect to auxiliary parameters. We focus on scalar theories, but the method is general and similar investigations extend to other theories.
String field theory-inspired algebraic structures in gauge theories
Zeitlin, Anton M.
2009-06-15
We consider gauge theories in a string field theory-inspired formalism. The constructed algebraic operations lead, in particular, to homotopy algebras of the related Batalin-Vilkovisky theories. We discuss an invariant description of the gauge fixing procedure and special algebraic features of gauge theories coupled to matter fields.
Planar Limit of Orientifold Field Theories and Emergent Center Symmetry
Armoni, Adi; Shifman, Mikhail; Unsal, Mithat
2007-12-05
We consider orientifold field theories (i.e. SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations) on R{sub 3} x S{sub 1} where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills. The latter has Z{sub N} center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from Z{sub N} symmetric to Z{sub N} broken phase applies. At the Lagrangian level the orientifold theories have at most a Z{sub 2} center. We discuss how the full Z{sub N} center symmetry dynamically emerges in the orientifold theories in the limit N {yields} {infinity}. In the confining phase the manifestation of this enhancement is the existence of stable k-strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.
Rearranging Pionless Effective Field Theory
Martin Savage; Silas Beane
2001-11-19
We point out a redundancy in the operator structure of the pionless effective field theory which dramatically simplifies computations. This redundancy is best exploited by using dibaryon fields as fundamental degrees of freedom. In turn, this suggests a new power counting scheme which sums range corrections to all orders. We explore this method with a few simple observables: the deuteron charge form factor, n p -> d gamma, and Compton scattering from the deuteron. Higher dimension operators involving electroweak gauge fields are not renormalized by the s-wave strong interactions, and therefore do not scale with inverse powers of the renormalization scale. Thus, naive dimensional analysis of these operators is sufficient to estimate their contribution to a given process.
Field theory of pattern identification
NASA Astrophysics Data System (ADS)
Agu, Masahiro
1988-06-01
Based on the psychological experimental fact that images in mental space are transformed into other images for pattern identification, a field theory of pattern identification of geometrical patterns is developed with the use of gauge field theory in Euclidean space. Here, the ``image'' or state function ψ[χ] of the brain reacting to a geometrical pattern χ is made to correspond to the electron's wave function in Minkowski space. The pattern identification of the pattern χ with the modified pattern χ+Δχ is assumed to be such that their images ψ[χ] and ψ[χ+Δχ] in the brain are transformable with each other through suitable transformation groups such as parallel transformation, dilatation, or rotation. The transformation group is called the ``image potential'' which corresponds to the vector potential of the gauge field. An ``image field'' derived from the image potential is found to be induced in the brain when the two images ψ[χ] and ψ[χ+Δχ] are not transformable through suitable transformation groups or gauge transformations. It is also shown that, when the image field exists, the final state of the image ψ[χ] is expected to be different, depending on the paths of modifications of the pattern χ leading to a final pattern. The above fact is interpreted as a version of the Aharonov and Bohm effect of the electron's wave function [A. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959)]. An excitation equation of the image field is also derived by postulating that patterns are identified maximally for the purpose of minimizing the number of memorized standard patterns.
Symmetries and strings in field theory and gravity
Banks, Tom; Seiberg, Nathan
2011-04-15
We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of Z{sub p} gauge theories shows that they are associated with an emergent Z{sub p} 1-form (Kalb-Ramond) gauge symmetry. This understanding leads us to uncover new observables and new phenomena in nonlinear {sigma} models. It also allows us to expand on Polchinski's classification of cosmic strings. We argue that in models of quantum gravity, there are no global symmetries, all continuous gauge symmetries are compact, and all charges allowed by Dirac quantization are present in the spectrum. These conjectures are not new, but we present them from a streamlined and unified perspective. Finally, our discussion about string charges and symmetries leads to a more physical and more complete understanding of recently found consistency conditions of supergravity.
The effective field theory of K-mouflage
NASA Astrophysics Data System (ADS)
Brax, Philippe; Valageas, Patrick
2016-01-01
We describe K-mouflage models of modified gravity using the effective field theory of dark energy. We show how the Lagrangian density K defining the K-mouflage models appears in the effective field theory framework, at both the exact fully nonlinear level and at the quadratic order of the effective action. We find that K-mouflage scenarios only generate the operator (δg00(u))n at each order n. We also reverse engineer K-mouflage models by reconstructing the whole effective field theory, and the full cosmological behaviour, from two functions of the Jordan-frame scale factor in a tomographic manner. This parameterisation is directly related to the implementation of the K-mouflage screening mechanism: screening occurs when K' is large in a dense environment such as the deep matter and radiation eras. In this way, K-mouflage can be easily implemented as a calculable subclass of models described by the effective field theory of dark energy which could be probed by future surveys.
Motion of small bodies in classical field theory
Gralla, Samuel E.
2010-04-15
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body's composition (and, e.g., black holes are allowed). The worldline 'left behind' by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the 'Bianchi identity' for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the ''monopoles'' of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of 'chameleon' bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.
From operator algebras to superconformal field theory
Kawahigashi, Yasuyuki
2010-01-15
We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of noncommutative geometry of Connes.
Hamiltonian dynamics of purely affine fields (Einstein-Schroedinger Theory)
NASA Astrophysics Data System (ADS)
Treder, H.-J.
The Lagrangian of the general-relativistic affine field theory of the non-symmetric connection field is the Schroedinger scalar density and the field variables (canonical coordinates) are Einstein's affine tensors. The field equations are the Einstein-Schroedinger equations, and the minors give by definition gmn = lambda-1Rmn, and lambda becomes the cosmological constant. The Hamiltonian density is the upsilon00-component of the Einstein energy-momentum complex, and the tensor-density components are the canonically conjugated momentum densities of the field coordinates. The canonical equations are (-g)-1/2Nlmnupsilon00 = 0, and we have no constraints. The affine field theory is invariant with respect to all transformations which preserve the Levi-Civita parallelism (Einstein's unified T-A group), and the field equations possess transposition invariance. The symmetry conditions Gammaimn = Gamma inm reduce the space to the general-relativistic Einstein spaces with Rik = Rki. The equation Rik = lambda gik yields Gammaikl = vector (i kl), and the pathes of test particles define geodesic world lines of the Einstein spaces.
Effective field theory, past and future
NASA Astrophysics Data System (ADS)
Weinberg, Steven
2016-02-01
I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In
Noncommutative Dipole Field Theories And Unitarity
Chiou, Dah-Wei; Ganor, Ori J.
2003-10-24
We extend the argument of Gomis and Mehen for violation of unitarity in field theories with space-time noncommutativity to dipole field theories. In dipole field theories with a timelike dipole vector, we present 1-loop amplitudes that violate the optical theorem. A quantum mechanical system with nonlocal potential of finite extent in time also shows violation of unitarity.
Topics in effective field theory as applied to lattice QCD
NASA Astrophysics Data System (ADS)
Smigielski, Brian
This thesis focuses on understanding aspects of hadronic physics using numerical and analytic computations which comprise the research fields of Lattice QCD and Effective Field Theories. Lattice QCD is a numerical approximation to QCD that is computed within a finite spacetime volume, a finite lattice spacing, and unphysically large values of the quark mass used to limit computational run time. Because Lattice QCD calculations are implemented with these constraints, it becomes necessary to understand how these constraints influence the physics if we are to extract physical observables. This requires the use and matching of an effective field theory for mesons and baryons which are the fundamental degrees of freedom of the effective field theory Lagrangian. We consider pion and nucleon interactions in Chapter 3 when computational demands force the use of small, spacetime lattices, and extract the axial charge of the nucleon. In Chapters 4 and 5 we examine systems of up to twelve particles of single species, pions or kaons, and mixed species systems of pions and kaons. From these systems we learn about the scattering lengths and three-body forces of these particles. These multi-particle systems also allow one to understand the behavior of finite density systems on the lattice. Lastly in Chapter 6, we examine parton distributions of the pion for a nonzero change in the pion's momentum. These are known as generalized parton distributions and reveal information regarding the valence quarks within a particular hadron. Before the advent of QCD, however, these particles were also known as partons.
NASA Astrophysics Data System (ADS)
Shen, Jian Qi
2016-05-01
A gravitational gauge theory with a spin-affine connection (Lorentz connection) as a rotational gauge potential (fundamental dynamical variable) is suggested for reformulating the theory of Stephenson-Kilmister-Yang gravity, in which the Einstein field equation of gravity is a first-integral solution of a spin-connection gravitational gauge field equation. A heavy intermediate field φ that accompanies a matter field \\varphi is introduced in order to remove the conventional dimensionful gravitational coupling. Such a \\varphi -φ coupling can lead to dimensionless gravitational coupling (i.e., the gravitational constant is dimensionless) in the present gravitational gauge field theory. A low-energy effective Lagrangian density for the matter field can be obtained by integrating out the accompanying heavy field in generating functional of path integral formalism, and therefore, a dimensionful gravitational coupling coefficient (Einstein gravitational constant) emerges. Such a dimensionless coupling of gravity, where the dimensionful coupling is emergent at low energies, is considered for scalar and spinor fields, which serve as gravitating matter fields (gravitational source). Though there are higher derivatives (e.g., third- and fourth-order partial derivatives) of the scalar and spinor fields in the low-energy effective Lagrangian densities, the ordinary equations of motion of the scalar and spinor fields can also be emergent from the present gravitational gauge theory. Therefore, the Einstein gravity can be recovered from the present gravitational gauge theory. In addition to the gravitational Lagrangian of the spacetime-rotational gauge potential (i.e., spin-affine connection), the Lagrangian of a spacetime-translational gauge potential (i.e., vierbein) is also constructed. Thus, the present dimensionless gravitational gauge coupling preserves local rotational and translational gauge symmetries. Since the spin-connection gravitational gauge field equation is a third-order differential equation of metric (the Einstein field equation of gravity is a first-integral solution), it could provide a new route to the vacuum energy cosmological constant problem.
Instantons in Lifshitz field theories
NASA Astrophysics Data System (ADS)
Fujimori, Toshiaki; Nitta, Muneto
2015-10-01
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4 + 1 dimensions, for which we take the Chern-Simons term as the superpotential.
Dual of the Janus solution: An interface conformal field theory
NASA Astrophysics Data System (ADS)
Clark, A. B.; Freedman, D. Z.; Karch, A.; Schnabl, M.
2005-03-01
We propose and study a specific gauge theory dual of the smooth, nonsupersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in Bak et al. [J. High Energy Phys., JHEPFG, 1029-8479 05 (2003) 072]. The dual field theory is N=4 SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator L' which is the fourth descendent of the primary TrX{IXJ} and closely related to the N=4 Lagrangian density. At the classical level supersymmetry is broken explicitly, but SO(3,2) conformal symmetry is preserved. We use conformal perturbation theory to study various correlation functions to first and second order in the discontinuity of g2YM, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value
Perturbative double field theory on general backgrounds
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Marques, Diego
2016-01-01
We develop the perturbation theory of double field theory around arbitrary solutions of its field equations. The exact gauge transformations are written in a manifestly background covariant way and contain at most quadratic terms in the field fluctuations. We expand the generalized curvature scalar to cubic order in fluctuations and thereby determine the cubic action in a manifestly background covariant form. As a first application we specialize this theory to group manifold backgrounds, such as S U (2 )≃S3 with H -flux. In the full string theory this corresponds to a Wess-Zumino-Witten background CFT. Starting from closed string field theory, the cubic action around such backgrounds has been computed before by Blumenhagen, Hassler, and Lüst. We establish precise agreement with the cubic action derived from double field theory. This result confirms that double field theory is applicable to arbitrary curved background solutions, disproving assertions in the literature to the contrary.
Unitary Fermi Gas, ɛ Expansion, and Nonrelativistic Conformal Field Theories
NASA Astrophysics Data System (ADS)
Nishida, Yusuke; Son, Dam Thanh
We review theoretical aspects of unitary Fermi gas (UFG), which has been realized in ultracold atom experiments. We first introduce the ɛ expansion technique based on a systematic expansion in terms of the dimensionality of space. We apply this technique to compute the thermodynamic quantities, the quasiparticle cum, and the criticl temperature of UFG. We then discuss consequences of the scale and conformal invariance of UFG. We prove a correspondence between primary operators in nonrelativistic conformal field theories and energy eigenstates in a harmonic potential. We use this correspondence to compute energies of fermions at unitarity in a harmonic potential. The scale and conformal invariance together with the general coordinate invariance constrains the properties of UFG. We show the vanishing bulk viscosities of UFG and derive the low-energy effective Lagrangian for the superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic scaling and conformal symmetries that can be in principle realized in ultracold atom experiments.
Physics of conformal field theories
NASA Astrophysics Data System (ADS)
Kats, Yevgeny
We study applied aspects of conformal field theories (CFTs) in two contexts. Chapter 1 explores "unparticle physics," which is the situation in which a hidden conformal sector (or one that becomes conformal at an infrared fixed point) couples to ordinary particles. We ask how to describe and compute processes generated by the self-interactions of the unparticle sector, whose physics is encoded in higher correlation functions of the CFT. We argue that the production of unparticle stuff in standard model processes due to the unparticle self-interactions can be decomposed using the conformal partial wave expansion into a sum over contributions from the production of various kinds of unparticle stuff, corresponding to the various primary conformal operators in the CFT, often different from those to which the standard model couples directly. We discuss inclusive and exclusive techniques for computing these processes. We exemplify our methods by computing the effects of self-interactions in the 2D Thirring model which is exactly solvable. We also study the Sommerfield model, that is a 2D theory of a massless fermion coupled to a massive vector boson which flows to the Thirring model at low energies. There we can see in detail how the production of the unparticle stuff from ordinary particles proceeds between the high-energy particle-like behavior of the unparticle sector and the low-energy unparticle behavior. In ordinary QCD, the short-distance perturbative physics of quarks and gluons turns into the physics of hadrons at large distances. We find that analogously to QCD there is a massive "hadron" in the spectrum of the Sommerfield model, but in sharp contrast with QCD there is also the unparticle stuff. Chapter 2 addresses strongly-coupled large-N CFTs that are accessible via the AdS/CFT correspondence. We study how the shear viscosity (at finite temperature) is affected by R2 corrections to the AdS action. We present an example of a 4D theory in which the conjectured bound on the viscosity-to-entropy ratio, eta/s≥1/47pi, is violated by 1/N corrections. The existence of such examples may be relevant to the QCD quark-gluon plasma which has eta/s≈1/4pi.
Soft theorems from effective field theory
NASA Astrophysics Data System (ADS)
Larkoski, Andrew J.; Neill, Duff; Stewart, Iain W.
2015-06-01
The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate this explicitly both at tree-level and at one-loop. The effective theory correctly describes these configurations, and we generalize the Low-Burnett-Kroll theorem into a new one-loop subleading soft theorem for amplitudes. Our analysis is presented in a manner that illustrates the wider utility of using effective theory techniques to understand the perturbative S-matrix.
Non-Abelian gauge field theory in scale relativity
Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry
2006-03-15
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.
Toward a gauge field theory of gravity.
NASA Astrophysics Data System (ADS)
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Leading three-baryon forces from SU(3) chiral effective field theory
NASA Astrophysics Data System (ADS)
Petschauer, Stefan; Kaiser, Norbert; Haidenbauer, Johann; Meißner, Ulf-G.; Weise, Wolfram
2016-01-01
Leading three-baryon forces are derived within SU(3) chiral effective field theory. Three classes of irreducible diagrams contribute: three-baryon contact terms, one-meson exchange, and two-meson exchange diagrams. We provide the minimal nonrelativistic terms of the chiral Lagrangian that contribute to these diagrams. SU(3) relations are given for the strangeness S =0 and -1 sectors. In the strangeness-zero sector we recover the well-known three-nucleon forces from chiral effective field theory. Explicit expressions for the Λ N N chiral potential in isospin space are presented.
Effective field theory calculation of second post-Newtonian binary dynamics
Gilmore, James B.; Ross, Andreas
2008-12-15
We use the effective field theory for gravitational bound states, proposed by Goldberger and Rothstein, to compute the interaction Lagrangian of a binary system at the second post-Newtonian order. Throughout the calculation, we use a metric parametrization based on a temporal Kaluza-Klein decomposition and test the claim by Kol and Smolkin that this parametrization provides important calculational advantages. We demonstrate how to use the effective field theory method efficiently in precision calculations, and we reproduce known results for the second post-Newtonian order equations of motion in harmonic gauge in a straightforward manner.
Lagrangian equations of motion of particles and photons in a Schwarzschild field
NASA Astrophysics Data System (ADS)
Ritus, V. I.
2015-11-01
The equations of motion of a particle in the gravitational field of a black hole are considered in a formulation that uses generalized coordinates, velocities, and accelerations and is convenient for finding the integrals of motion. The equations are rewritten in terms of the physical velocities and accelerations measured in the Schwarzschild frame by a stationary observer using proper local length and time standards. The attractive force due to the field and the centripetal acceleration of a particle is proportional to the particle kinetic energy m/\\sqrt{1 - v^2}, consistently with the fact that the particle kinetic energy and the photon energy \\hbarω in the field increase by the same factor compared with their values without a field. The attraction exerted on particles and photons by a gravitational field source is proportional to their kinetic energies. The particle trajectory in the ultrarelativistic limit v \\to 1 coincides with the photon trajectory.
Boson formulation of fermion field theories
Ha, Y.K.
1984-04-15
The nonperturbative connection between a canonical Fermi field and a canonical Bose field in two dimensions is developed and its validity verified according to the tenets of quantum field theory. We advocate the point of view that a boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. Many features of the massless theory, such as dynamical mass generation with asymptotic-freedom behavior, hidden chiral symmetry, and connections with models of apparently different internal symmetries, are readily transparent through such fermion-boson metamorphosis.
NASA Astrophysics Data System (ADS)
Albaugh, Alex; Demerdash, Omar; Head-Gordon, Teresa
2015-11-01
We have adapted a hybrid extended Lagrangian self-consistent field (EL/SCF) approach, developed for time reversible Born Oppenheimer molecular dynamics for quantum electronic degrees of freedom, to the problem of classical polarization. In this context, the initial guess for the mutual induction calculation is treated by auxiliary induced dipole variables evolved via a time-reversible velocity Verlet scheme. However, we find numerical instability, which is manifested as an accumulation in the auxiliary velocity variables, that in turn results in an unacceptable increase in the number of SCF cycles to meet even loose convergence tolerances for the real induced dipoles over the course of a 1 ns trajectory of the AMOEBA14 water model. By diagnosing the numerical instability as a problem of resonances that corrupt the dynamics, we introduce a simple thermostating scheme, illustrated using Berendsen weak coupling and Nose-Hoover chain thermostats, applied to the auxiliary dipole velocities. We find that the inertial EL/SCF (iEL/SCF) method provides superior energy conservation with less stringent convergence thresholds and a correspondingly small number of SCF cycles, to reproduce all properties of the polarization model in the NVT and NVE ensembles accurately. Our iEL/SCF approach is a clear improvement over standard SCF approaches to classical mutual induction calculations and would be worth investigating for application to ab initio molecular dynamics as well.
Descent relations in cubic superstring field theory
NASA Astrophysics Data System (ADS)
Aref'eva, I. Y.; Gorbachev, R.; Medvedev, P. B.; Rychkov, D. V.
2008-01-01
The descent relations between string field theory (SFT) vertices are characteristic relations of the operator formulation of SFT and they provide self-consistency of this theory. The descent relations langleV2|V1rangle and langleV3|V1rangle in the NS fermionic string field theory in the κ and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.
Classical adiabatic holonomy in field theory
Gozzi, E. ); Rohrlich, D. ); Thacker, W.D. )
1990-10-15
In this paper we develop the notion of adiabatic holonomy in {ital classical} fermionic field theory and apply it to chiral gauge theory. In chiral gauge theory the {ital classical} adiabatic holonomy leads to a deformation of the Poisson algebra of translation generators in the space of gauge fields and to an additional term in the Poisson brackets among gauge-transformation generators. We study all this in detail in a (1+1)-dimensional model.
Introduction to conformal field theory and string theory
Dixon, L.J.
1989-12-01
These lectures are meant to provide a brief introduction to conformal field theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available, and most of these go in to much more detail than I will be able to here. 52 refs., 11 figs.
E11 and exceptional field theory
NASA Astrophysics Data System (ADS)
Tumanov, Alexander G.; West, Peter
2016-04-01
We argue that the exceptional field theory is a truncation of the nonlinear realisation of the semi-direct product of E11 and its first fundamental as proposed in 2003. Evaluating the simple equations of the E11 approach, and using the commutators of the E11 algebra, we find the local variations of the fields of exceptional field theory after making a radical truncation. This procedure does not respect any of the higher level E11 symmetries and so these are lost. We suggest that the need for the section condition in the exceptional field theory could be a consequence of the truncation.
Motion of small bodies in classical field theory
NASA Astrophysics Data System (ADS)
Gralla, Samuel E.
2010-04-01
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body’s composition (and, e.g., black holes are allowed). The worldline “left behind” by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the “Bianchi identity” for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the “monopoles” of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of “chameleon” bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.
Generating functionals and Lagrangian partial differential equations
Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin
2013-08-15
The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an example of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.
Discrete Pluriharmonic Functions as Solutions of Linear Pluri-Lagrangian Systems
NASA Astrophysics Data System (ADS)
Bobenko, A. I.; Suris, Yu. B.
2015-05-01
Pluri-Lagrangian systems are variational systems with the multi-dimensional consistency property. This notion has its roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics, in the theory of variational symmetries going back to Noether and in the theory of discrete integrable systems. A d-dimensional pluri-Lagrangian problem can be described as follows: given a d-form L on an m-dimensional space, m > d, whose coefficients depend on a function u of m independent variables (called field), find those fields u which deliver critical points to the action functionals for any d-dimensional manifold Σ in the m-dimensional space. We investigate discrete 2-dimensional linear pluri-Lagrangian systems, i.e., those with quadratic Lagrangians L. The action is a discrete analogue of the Dirichlet energy, and solutions are called discrete pluriharmonic functions. We classify linear pluri-Lagrangian systems with Lagrangians depending on diagonals. They are described by generalizations of the star-triangle map. Examples of more general quadratic Lagrangians are also considered.
Weyl's Lagrangian in teleparallel form
Burnett, James; Vassiliev, Dmitri
2009-10-15
The Weyl Lagrangian is the massless Dirac Lagrangian. The dynamical variable in the Weyl Lagrangian is a spinor field. We provide a mathematically equivalent representation in terms of a different dynamical variable - the coframe (an orthonormal tetrad of covector fields). We show that when written in terms of this dynamical variable, the Weyl Lagrangian becomes remarkably simple: it is the wedge product of axial torsion of the teleparallel connection with a teleparallel lightlike element of the coframe. We also examine the issues of U(1)-invariance and conformal invariance. Examination of the latter motivates us to introduce a positive scalar field (equivalent to a density) as an additional dynamical variable; this makes conformal invariance self-evident.
The theory of the Galactic magnetic field
NASA Technical Reports Server (NTRS)
Zweibel, Ellen G.
1987-01-01
The paper discusses the role of the magnetic field in determining the large scale structure and dynamics of the interstellar medium. It then discusses the origin and maintenance of the Galactic field. The two major competing theories are that the field is primordial and connected to an intergalactic field or that the field is removed from and regenerated within the Galaxy. Finally, cosmic ray acceleration and confinement in the interstellar medium are discussed.
On causality in polymer scalar field theory
NASA Astrophysics Data System (ADS)
García-Chung, Angel A.; Morales-Técotl, Hugo A.
2011-10-01
The properties of spacetime corresponding to a proposed quantum gravity theory might modify the high energy behavior of quantum fields. Motivated by loop quantum gravity, recently, Hossain et al [1] have considered a polymer field algebra that replaces the standard canonical one in order to calculate the propagator of a real scalar field in flat spacetime. This propagator features Lorentz violations. Motivated by the relation between Lorentz invariance and causality in standard Quantum Field Theory, in this work we investigate the causality behavior of the polymer scalar field.
Twisted Poincare invariant quantum field theories
Balachandran, A. P.; Qureshi, B. A.; Pinzul, A.
2008-01-15
It is by now well known that the Poincare group acts on the Moyal plane with a twisted coproduct. Poincare invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a twisted Poincare action in quantum theories on the Moyal plane. We develop quantum field theories invariant under the twisted action from the representations of the Poincare group, ensuring also the invariance of the S-matrix under the twisted action of the group. A significant new contribution here is the construction of the Poincare generators using quantum fields.
Zero Dimensional Field Theory of Tachyon Matter
Dimitrijevic, D. D.; Djordjevic, G. S.
2007-04-23
The first issue about the object (now) called tachyons was published almost one century ago. Even though there is no experimental evidence of tachyons there are several reasons why tachyons are still of interest today, in fact interest in tachyons is increasing. Many string theories have tachyons occurring as some of the particles in the theory. In this paper we consider the zero dimensional version of the field theory of tachyon matter proposed by A. Sen. Using perturbation theory and ideas of S. Kar, we demonstrate how this tachyon field theory can be connected with a classical mechanical system, such as a massive particle moving in a constant field with quadratic friction. The corresponding Feynman path integral form is proposed using a perturbative method. A few promising lines for further applications and investigations are noted.
Relativistic mean-field theory
NASA Astrophysics Data System (ADS)
Meng, Jie; Ring, Peter; Zhao, Pengwei
In this chapter, the covariant energy density functional is constructed with both the meson-exchange and the point-coupling pictures. Several widely used functionals with either nonlinear or density-dependent effective interactions are introduced. The applications of covariant density functional theory are demonstrated for infinite nuclear matter and finite nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes. Finally, a relativistic description of the nuclear landscape has been discussed, which is not only important for nuclear structure, but also important for nuclear astrophysics, where we are facing the problem of a reliable extrapolation to the very neutron-rich nuclei.
Quantum statistical correlations in thermal field theories: Boundary effective theory
Bessa, A.; Brandt, F. T.; Carvalho, C. A. A. de; Fraga, E. S.
2010-09-15
We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field {phi}{sub c}, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schroedinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field {phi}{sub c}, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.
Moduli spaces and topological quantum field theories
Sonnenschein, J.
1989-07-01
We show how to construct a topological quantum field theory which corresponds to a given moduli space. This method is applied to several cases. In particular we discuss the moduli space of flat gauge connections over a Riemann surface which is related to the phase space of the Chern-Simons theory. The observables of these theories are derived. Geometrical properties are invoked to prove that the global invariants are not trivial. 14 refs., 3 tabs.
Lagrangian postprocessing of computational hemodynamics
Shadden, Shawn C.; Arzani, Amirhossein
2014-01-01
Recent advances in imaging, modeling and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows. PMID:25059889
Dark energy or modified gravity? An effective field theory approach
Bloomfield, Jolyon; Flanagan, Éanna É.; Park, Minjoon; Watson, Scott E-mail: eef3@cornell.edu E-mail: gswatson@syr.edu
2013-08-01
We take an Effective Field Theory (EFT) approach to unifying existing proposals for the origin of cosmic acceleration and its connection to cosmological observations. Building on earlier work where EFT methods were used with observations to constrain the background evolution, we extend this program to the level of the EFT of the cosmological perturbations — following the example from the EFT of Inflation. Within this framework, we construct the general theory around an assumed background which will typically be chosen to mimic ΛCDM, and identify the parameters of interest for constraining dark energy and modified gravity models with observations. We discuss the similarities to the EFT of Inflation, but we also identify a number of subtleties including the relationship between the scalar perturbations and the Goldstone boson of the spontaneously broken time translations. We present formulae that relate the parameters of the fundamental Lagrangian to the speed of sound, anisotropic shear stress, effective Newtonian constant, and Caldwell's varpi parameter, emphasizing the connection to observations. It is anticipated that this framework will be of use in constraining individual models, as well as for placing model-independent constraints on dark energy and modified gravity model building.
Numerical calculations in quantum field theories
Rebbi, C.
1984-01-01
Four lecture notes are included: (1) motivation for numerical calculations in Quantum Field Theory; (2) numerical simulation methods; (3) Monte Carlo studies of Quantum Chromo Dynamics; and (4) systems with fermions. 23 references. (WHK)
Pure field theories and MACSYMA algorithms
NASA Technical Reports Server (NTRS)
Ament, W. S.
1977-01-01
A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.
Weyl's Abandonment of Unified Field Theory
NASA Astrophysics Data System (ADS)
Sieroka, Norman
2015-01-01
In 1918, Hermann Weyl proposed a generalisation of Riemannian geometry, in order to unify general relativity and electrodynamics. This paper investigates the physical, mathematical and philosophical reasons for his subsequent abandonment of any such attempt towards a unified field theory.
Effective Field Theory in Nuclear Astrophysics
NASA Astrophysics Data System (ADS)
Chen, Jiunn-Wei
2001-12-01
I review high precision effective field theory calculations to np → dγ, relevant for big-bang nucleosynthesis and νd inelastic scattering relevant for the solar neutrino detection processes employed by Sudbury neutrino observatory.
Generalized extended Lagrangian Born-Oppenheimer molecular dynamics
Niklasson, Anders M. N. Cawkwell, Marc J.
2014-10-28
Extended Lagrangian Born-Oppenheimer molecular dynamics based on Kohn-Sham density functional theory is generalized in the limit of vanishing self-consistent field optimization prior to the force evaluations. The equations of motion are derived directly from the extended Lagrangian under the condition of an adiabatic separation between the nuclear and the electronic degrees of freedom. We show how this separation is automatically fulfilled and system independent. The generalized equations of motion require only one diagonalization per time step and are applicable to a broader range of materials with improved accuracy and stability compared to previous formulations.
{N}=3 four dimensional field theories
NASA Astrophysics Data System (ADS)
García-Etxebarria, Iñaki; Regalado, Diego
2016-03-01
We introduce a class of four dimensional field theories constructed by quotienting ordinary {N}=4 U(N ) SYM by particular combinations of R-symmetry and SL(2, ℤ) automorphisms. These theories appear naturally on the worldvolume of D3 branes probing terminal singularities in F-theory, where they can be thought of as non-perturbative generalizations of the O3 plane. We focus on cases preserving only 12 supercharges, where the quotient gives rise to theories with coupling fixed at a value of order one. These constructions possess an unconventional large N limit described by a non-trivial F-theory fibration with base AdS 5 × (S 5/ ℤ k ). Upon reduction on a circle the {N}=3 theories flow to well-known {N}=6 ABJM theories.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Effective field theory for 4He
NASA Astrophysics Data System (ADS)
Carmona, J. M.; Jimnez, S.; Polonyi, J.; Tarancn, A.
2006-01-01
We introduce an effective scalar field theory to describe the He4 phase diagram, which can be considered as a generalization of the XY model which gives the usual ? transition. This theory results from a Ginzburg-Landau Hamiltonian with higher order derivatives, which allow one to produce transitions between the superfluid, normal liquid, and solid phases of He4 . Mean field and Monte Carlo analyses suggest that this model is able to reproduce the main qualitative features of He4 phase transitions.
Conserved currents of double field theory
NASA Astrophysics Data System (ADS)
Blair, Chris D. A.
2016-04-01
We find the conserved current associated to invariance under generalised diffeomorphisms in double field theory. This can be used to define a generalised Komar integral. We comment on its applications to solutions, in particular to the fundamental string/pp-wave. We also discuss the current in the context of Scherk-Schwarz compactifications. We calculate the current for both the original double field theory action, corresponding to the NSNS sector alone, and for the RR sector.
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. PMID:22654052
The zero-bin and mode factorization in quantum field theory
NASA Astrophysics Data System (ADS)
Manohar, Aneesh V.; Stewart, Iain W.
2007-10-01
We study a Lagrangian formalism that avoids double counting in effective field theories where distinct fields are used to describe different infrared momentum regions for the same particle. The formalism leads to extra subtractions in certain diagrams and to a new way of thinking about factorization of modes in quantum field theory. In nonrelativistic field theories, the subtractions remove unphysical pinch singularities in box-type diagrams, and give a derivation of the known pullup mechanism between soft and ultrasoft fields which is required by the renormalization group evolution. In a field theory for energetic particles, the soft-collinear effective theory (SCET), the subtractions allow the theory to be defined with different infrared and ultraviolet regulators, remove double counting between soft, ultrasoft, and collinear modes, and give results which reproduce the infrared divergences of the full theory. Our analysis shows that convolution divergences in factorization formulas occur due to an overlap of momentum regions. We propose a method that avoids this double counting, which helps to resolve a long-standing puzzle with singularities in collinear factorization in QCD. The analysis gives evidence for a factorization in rapidity space in exclusive decays.
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
2006-02-25
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
Entanglement entropy in warped conformal field theories
NASA Astrophysics Data System (ADS)
Castro, Alejandra; Hofman, Diego M.; Iqbal, Nabil
2016-02-01
We present a detailed discussion of entanglement entropy in (1+1)-dimensional Warped Conformal Field Theories (WCFTs). We implement the Rindler method to evaluate entanglement and Renyi entropies for a single interval and along the way we interpret our results in terms of twist field correlation functions. Holographically a WCFT can be described in terms of Lower Spin Gravity, a SL (2, ℝ) × U (1) Chern-Simons theory in three dimensions. We show how to obtain the universal field theory results for entanglement in a WCFT via holography. For the geometrical description of the theory we introduce the concept of geodesic and massive point particles in the warped geometry associated to Lower Spin Gravity. In the Chern-Simons description we evaluate the appropriate Wilson line that captures the dynamics of a massive particle.
Group field theory in dimension 4 -?
NASA Astrophysics Data System (ADS)
Carrozza, Sylvain
2015-03-01
Building on an analogy with ordinary scalar field theories, an ? -expansion for rank-3 tensorial group field theories with gauge invariance condition is introduced. This allows us to continuously interpolate between the dimension four group SU (2 )U (1 ) and the dimension three SU(2). In the first situation, there is a unique marginal ?4 coupling constant, but in contrast to ordinary scalar field theory this model is asymptotically free. In the SU(2) case, the presence of two marginally relevant ?6 coupling constants and one ?4 super-renormalizable interaction spoils this interesting property. However, the existence of a nontrivial fixed point is established in dimension 4 -? , hence suggesting that the SU(2) theory might be asymptotically safe. To pave the way to future nonperturbative calculations, the present perturbative results are discussed in the framework of the effective average action.
The Theory of Quantized Fields. II
DOE R&D Accomplishments Database
Schwinger, J.
1951-01-01
The arguments leading to the formulation of the Action Principle for a general field are presented. In association with the complete reduction of all numerical matrices into symmetrical and anti-symmetrical parts, the general field is decomposed into two sets, which are identified with Bose-Einstein and Fermi-Dirac fields. The spin restriction on the two kinds of fields is inferred from the time reflection invariance requirement. The consistency of the theory is verified in terms of a criterion involving the various generators of infinitesimal transformations. Following a discussion of charged fields, the electromagnetic field is introduced to satisfy the postulate of general gauge invariance. As an aspect of the latter, it is recognized that the electromagnetic field and charged fields are not kinematically independent. After a discussion of the field-strength commutation relations, the independent dynamical variable of the electromagnetic field are exhibited in terms of a special gauge.
Casimir Effects in Renormalizable Quantum Field Theories
NASA Astrophysics Data System (ADS)
Graham, Noah; Jaffe, Robert L.; Weigel, Herbert
We present a framework for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.
Conformal field theory on affine Lie groups
Clubok, K.S.
1996-04-01
Working directly on affine Lie groups, we construct several new formulations of the WZW model, the gauged WZW model, and the generic affine-Virasoro action. In one formulation each of these conformal field theories (CFTs) is expressed as a one-dimensional mechanical system whose variables are coordinates on the affine Lie group. When written in terms of the affine group element, this formulation exhibits a two-dimensional WZW term. In another formulation each CFT is written as a two-dimensional field theory, with a three- dimensional WZW term, whose fields are coordinates on the affine group. On the basis of these equivalent formulations, we develop a translation dictionary in which the new formulations on the affine Lie group are understood as mode formulations of the conventional formulations on the Lie group. Using this dictionary, we also express each CFT as a three-dimensional field theory on the Lie group with a four-dimensional WZW term. 36 refs.
Nonequilibrium statistical field theory for classical particles: Basic kinetic theory
NASA Astrophysics Data System (ADS)
Viermann, Celia; Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias
2015-06-01
Recently Mazenko and Das and Mazenko [Phys. Rev. E 81, 061102 (2010), 10.1103/PhysRevE.81.061102; J. Stat. Phys. 149, 643 (2012), 10.1007/s10955-012-0610-y; J. Stat. Phys. 152, 159 (2013), 10.1007/s10955-013-0755-3; Phys. Rev. E 83, 041125 (2011), 10.1103/PhysRevE.83.041125] introduced a nonequilibrium field-theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.
Nonequilibrium statistical field theory for classical particles: Basic kinetic theory.
Viermann, Celia; Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias
2015-06-01
Recently Mazenko and Das and Mazenko [Phys. Rev. E 81, 061102 (2010); J. Stat. Phys. 149, 643 (2012); J. Stat. Phys. 152, 159 (2013); Phys. Rev. E 83, 041125 (2011)] introduced a nonequilibrium field-theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits. PMID:26172674
Topics in Supersymmetric Quantum Field Theory
NASA Astrophysics Data System (ADS)
Dumitrescu, Thomas
This thesis describes several new tools for analyzing supersymmetric quantum field theories, focusing on theories with four supercharges in three and four dimensions. In chapter two, we discuss supercurrents, supersymmetry multiplets that include the energy-momentum tensor. Physically, different supercurrents give rise to different brane charges in the supersymmetry algebra. They also encode different ways of placing supersymmetric field theories on a curved manifold. Under certain conditions this procedure preserves some of the supersymmetry. In chapter three, we explore these conditions for the case of four-dimensional N = 1 theories with a U(1)R symmetry. In particular, we find that a manifold admits a single supercharge if and only if it is Hermitian. In chapter four, we shift the focus to three-dimensional field theories. We study Chern-Simons contact terms -- contact terms of conserved currents and the energy-momentum tensor, which are associated with Chern-Simons terms for background fields. While the integer parts of these contact terms are ambiguous, their fractional parts constitute new meaningful observables. In N = 2 supersymmetric theories with a U(1) R symmetry certain Chern-Simons contact terms can lead to a novel superconformal anomaly. In chapter five, we use this understanding to elucidate the structure of the free energy F of these theories on a three sphere. In particular, we prove the F-maximization principle for N = 2 superconformal theories. We also explain why computing F via localization leads to a complex answer, even though we expect it to be real in unitary theories.
Pauli-Villars regularization of field theories on the light front
Hiller, John R.
2010-12-22
Four-dimensional quantum field theories generally require regularization to be well defined. This can be done in various ways, but here we focus on Pauli-Villars (PV) regularization and apply it to nonperturbative calculations of bound states. The philosophy is to introduce enough PV fields to the Lagrangian to regulate the theory perturbatively, including preservation of symmetries, and assume that this is sufficient for the nonperturbative case. The numerical methods usually necessary for nonperturbative bound-state problems are then applied to a finite theory that has the original symmetries. The bound-state problem is formulated as a mass eigenvalue problem in terms of the light-front Hamiltonian. Applications to quantum electrodynamics are discussed.
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U{sub q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun{sub q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Non Perturbative Aspects of Field Theory
Bashir, A.
2009-04-20
For any quantum field theory (QFT), there exists a set of Schwinger-Dyson equations (SDE) for all its Green functions. However, it is not always straight forward to extract quantitatively exact physical information from this set of equations, especially in the non perturbative regime. The situation becomes increasingly complex with growing number of external legs. I give a qualitative account of the hunt for the non perturbative Green functions in gauge theories.
Magnetic monopoles in field theory and cosmology.
Rajantie, Arttu
2012-12-28
The existence of magnetic monopoles is predicted by many theories of particle physics beyond the standard model. However, in spite of extensive searches, there is no experimental or observational sign of them. I review the role of magnetic monopoles in quantum field theory and discuss their implications for particle physics and cosmology. I also highlight their differences and similarities with monopoles found in frustrated magnetic systems. PMID:23166376
A noncommutative deformation of topological field theory
NASA Astrophysics Data System (ADS)
García-Compeán, Hugo; Paniagua, Pablo
2005-04-01
Cohomological Yang Mills theory is formulated on a noncommutative differentiable four manifold through the θ-deformation of its corresponding BRST algebra. The resulting noncommutative field theory is a natural setting to define the θ-deformation of Donaldson invariants and they are interpreted as a mapping between the Chevalley Eilenberg homology of noncommutative spacetime and the Chevalley Eilenberg cohomology of noncommutative moduli of instantons. In the process we find that in the weak coupling limit the quantum theory is localized at the moduli space of noncommutative instantons.
Experimental Bounds on Classical Random Field Theories
NASA Astrophysics Data System (ADS)
Peters, Joffrey K.; Fan, Jingyun; Migdall, Alan L.; Polyakov, Sergey V.
2015-07-01
Alternative theories to quantum mechanics motivate important fundamental tests of our understanding and descriptions of the smallest physical systems. Here, using spontaneous parametric downconversion as a heralded single-photon source, we place experimental limits on a class of alternative theories, consisting of classical field theories which result in power-dependent normalized correlation functions. In addition, we compare our results with standard quantum mechanical interpretations of our spontaneous parametric downconversion source over an order of magnitude in intensity. Our data match the quantum mechanical expectations, and do not show a statistically significant dependence on power, limiting quantum mechanics alternatives which require power-dependent autocorrelation functions.
Conformal Field Theories in Fractional Dimensions
NASA Astrophysics Data System (ADS)
El-Showk, Sheer; Paulos, Miguel; Poland, David; Rychkov, Slava; Simmons-Duffin, David; Vichi, Alessandro
2014-04-01
We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary conformal field theories connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of ϕ4 theory in the ɛ expansion.
Diagrammar in classical scalar field theory
Cattaruzza, E.; Gozzi, E.; Francisco Neto, A.
2011-09-15
In this paper we analyze perturbatively a g{phi}{sup 4}classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost 'identical' formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem. - Highlights: > We provide the Feynman diagrams of perturbation theory for a classical field theory. > We give a super-formalism which links the quantum diagrams to the classical ones. > We check perturbatively the fluctuation-dissipation theorem.
Supergeometry in Locally Covariant Quantum Field Theory
NASA Astrophysics Data System (ADS)
Hack, Thomas-Paul; Hanisch, Florian; Schenkel, Alexander
2016-03-01
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc to S* Alg to the category of super-*-algebras, which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc to eS* Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1|1-dimensions and the free Wess-Zumino model in 3|2-dimensions.
Arrival time in quantum field theory
NASA Astrophysics Data System (ADS)
Wang, Zhi-Yong; Xiong, Cai-Dong; He, Bing
2008-09-01
Via the proper-time eigenstates (event states) instead of the proper-mass eigenstates (particle states), free-motion time-of-arrival theory for massive spin-1/2 particles is developed at the level of quantum field theory. The approach is based on a position-momentum dual formalism. Within the framework of field quantization, the total time-of-arrival is the sum of the single event-of-arrival contributions, and contains zero-point quantum fluctuations because the clocks under consideration follow the laws of quantum mechanics.
Effective field theory for deformed atomic nuclei
NASA Astrophysics Data System (ADS)
Papenbrock, T.; Weidenmüller, H. A.
2016-05-01
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Near-field optical thin microcavity theory
NASA Astrophysics Data System (ADS)
Wu, Jiu Hui; Hou, Jiejie
2016-01-01
The thin microcavity theory for near-field optics is proposed in this study. By applying the power flow theorem and the variable theorem,the bi-harmonic differential governing equation for electromagnetic field of a three-dimensional thin microcavity is derived for the first time. Then by using the Hankel transform, this governing equation is solved exactly and all the electromagnetic components inside and outside the microcavity can be obtained accurately. According to the above theory, the near-field optical diffraction from a subwavelength aperture embedded in a thin conducting film is investigated, and numerical computations are performed to illustrate the edge effect by an enhancement factor of 1.8 and the depolarization phenomenon of the near-field transmission in terms of the distance from the film surface. This thin microcavity theory is verified by the good agreement between our results and those in the previous literatures. The thin microcavity theory presented in the study should be useful in the possible applications of the thin microcavities in near-field optics and thin-film optics.
Astrophysical data analysis with information field theory
Enßlin, Torsten
2014-12-05
Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.
Symmetry analysis for anisotropic field theories
Parra, Lorena; Vergara, J. David
2012-08-24
The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.
Singular Lagrangians. Classical dynamics and quantization. Lectures for young scientists
NASA Astrophysics Data System (ADS)
Nesterenko, V. V.; Chervyakov, A. M.
The lectures are devoted to the classical and quantum dynamics of the systems described by singular (or degenerate) Lagrangians. The complete set of the Hamiltonian constraints is constructed in the framework of the Lagrangian formalism. The equations of motion in the phase space are derived by taking into account all the constraints in the theory. It is proved that the dynamic on the physical submanifold of the phase space has the Hamiltonian form. On lectures the second Noether theorem is widely used. On its basis the properties of the Poisson brackets of the primary constraints are investigated and the invariance of the Lagrangian constraints during evolution is proved. The setting of the Cauchy problem in the theories with singular Lagrangians is discussed. The quantization of the systems with constraints is carried out by the functional integration in the phase space. There is considered the most general case of the first class and the second class constraints with an explicit time dependence. The gauge conditions may be noninvoluntary and time dependent. The material is illustrated by some examples (relativistic point particle, relativistic string, electromagnetic field, and Yang-Mills fields).
COLAcode: COmoving Lagrangian Acceleration code
NASA Astrophysics Data System (ADS)
Tassev, Svetlin V.
2016-02-01
COLAcode is a serial particle mesh-based N-body code illustrating the COLA (COmoving Lagrangian Acceleration) method; it solves for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories calculated in Lagrangian Perturbation Theory (LPT). It differs from standard N-body code by trading accuracy at small-scales to gain computational speed without sacrificing accuracy at large scales. This is useful for generating large ensembles of accurate mock halo catalogs required to study galaxy clustering and weak lensing; such catalogs are needed to perform detailed error analysis for ongoing and future surveys of LSS.
Lagrangian continuum dynamics in ALEGRA.
Wong, Michael K. W.; Love, Edward
2007-12-01
Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.
Double field theory: a pedagogical review
NASA Astrophysics Data System (ADS)
Aldazabal, Gerardo; Marqués, Diego; Núñez, Carmen
2013-08-01
Double field theory (DFT) is a proposal to incorporate T-duality, a distinctive symmetry of string theory, as a symmetry of a field theory defined on a double configuration space. The aim of this review is to provide a pedagogical presentation of DFT and its applications. We first introduce some basic ideas on T-duality and supergravity in order to proceed to the construction of generalized diffeomorphisms and an invariant action on the double space. Steps towards the construction of a geometry on the double space are discussed. We then address generalized Scherk-Schwarz compactifications of DFT and their connection to gauged supergravity and flux compactifications. We also discuss U-duality extensions and present a brief parcours on worldsheet approaches to DFT. Finally, we provide a summary of other developments and applications that are not discussed in detail in the review.
Prequantum Classical Statistical Field Theory: Fundamentals
Khrennikov, Andrei
2011-03-28
We present fundamentals of a prequantum model with hidden variables of the classical field type. In some sense this is the comeback of classical wave mechanics. Our approach also can be considered as incorporation of quantum mechanics into classical signal theory. All quantum averages (including correlations of entangled systems) can be represented as classical signal averages and correlations.
Cross Sections From Scalar Field Theory
NASA Technical Reports Server (NTRS)
Norbury, John W.; Dick, Frank; Norman, Ryan B.; Nasto, Rachel
2008-01-01
A one pion exchange scalar model is used to calculate differential and total cross sections for pion production through nucleon- nucleon collisions. The collisions involve intermediate delta particle production and decay to nucleons and a pion. The model provides the basic theoretical framework for scalar field theory and can be applied to particle production processes where the effects of spin can be neglected.
Lagrangian fronts in the ocean
NASA Astrophysics Data System (ADS)
Prants, S. V.; Budyansky, M. V.; Uleysky, M. Yu.
2014-05-01
We introduce the concept of Lagrangian fronts (LFs) in the ocean and describe their importance for analyzing water mixing and transport and the specific features and differences from hydrological fronts. A method of calculating LFs in a given velocity field is proposed. Based on altimeter velocity fields from AVISO data in the northwestern Pacific, we calculate the Lagrangian synoptic maps and identify LFs of different spatial and temporal scales. Using statistical analysis of saury catches in different years according to the Goskomrybolovstvo (State Fisheries Committee of the Russian Federation), we show that LFs can serve as good indicators of places that are favorable for fishing.
Monte Carlo approaches to effective field theories
Carlson, J. ); Schmidt, K.E. . Dept. of Physics)
1991-01-01
In this paper, we explore the application of continuum Monte Carlo methods to effective field theory models. Effective field theories, in this context, are those in which a Fock space decomposition of the state is useful. These problems arise both in nuclear and condensed matter physica. In nuclear physics, much work has been done on effective field theories of mesons and baryons. While the theories are not fundamental, they should be able to describe nuclear properties at low energy and momentum scales. After describing the methods, we solve two simple scalar field theory problems; the polaron and two nucleons interacting through scalar meson exchange. The methods presented here are rather straightforward extensions of methods used to solve quantum mechanics problems. Monte Carlo methods are used to avoid the truncation inherent in a Tamm-Dancoff approach and its associated difficulties. Nevertheless, the methods will be most valuable when the Fock space decomposition of the states is useful. Hence, while they are not intended for ab initio studies of QCD, they may prove valuable in studies of light nuclei, or for systems of interacting electrons and phonons. In these problems a Fock space decomposition can be used to reduce the number of degrees of freedom and to retain the rotational symmetries exactly. The problems we address here are comparatively simple, but offer useful initial tests of the method. We present results for the polaron and two non-relativistic nucleons interacting through scalar meson exchange. In each case, it is possible to integrate out the boson degrees of freedom exactly, and obtain a retarded form of the action that depends only upon the fermion paths. Here we keep the explicit bosons, though, since we would like to retain information about the boson components of the states and it will be necessary to keep these components in order to treat non-scalar of interacting bosonic fields.
Effective Field Theory for Jet Processes
NASA Astrophysics Data System (ADS)
Becher, Thomas; Neubert, Matthias; Rothen, Lorena; Shao, Ding Yu
2016-05-01
Processes involving narrow jets receive perturbative corrections enhanced by logarithms of the jet opening angle and the ratio of the energies inside and outside the jets. Analyzing cone-jet processes in effective field theory, we find that in addition to soft and collinear fields their description requires degrees of freedom that are simultaneously soft and collinear to the jets. These collinear-soft particles can resolve individual collinear partons, leading to a complicated multi-Wilson-line structure of the associated operators at higher orders. Our effective field theory provides, for the first time, a factorization formula for a cone-jet process, which fully separates the physics at different energy scales. Its renormalization-group equations control all logarithmically enhanced higher-order terms, in particular also the nonglobal logarithms.
Quantum stability of chameleon field theories.
Upadhye, Amol; Hu, Wayne; Khoury, Justin
2012-07-27
Chameleon scalar fields are dark-energy candidates which suppress fifth forces in high density regions of the Universe by becoming massive. We consider chameleon models as effective field theories and estimate quantum corrections to their potentials. Requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound m<0.0073(ρ/10 g cm(-3))(1/3) eV for gravitational-strength coupling whereas fifth force experiments place a lower bound of m>0.0042 eV. An improvement of less than a factor of two in the range of fifth force experiments could test all classical chameleon field theories whose quantum corrections are well controlled and couple to matter with nearly gravitational strength regardless of the specific form of the chameleon potential. PMID:23006073
A computational theory of visual receptive fields.
Lindeberg, Tony
2013-12-01
A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space-time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative agreement are obtained for (i) spatial on-center/off-surround and off-center/on-surround receptive fields in the fovea and the LGN, (ii) simple cells with spatial directional preference in V1, (iii) spatio-chromatic double-opponent neurons in V1, (iv) space-time separable spatio-temporal receptive fields in the LGN and V1, and (v) non-separable space-time tilted receptive fields in V1, all within the same unified theory. In addition, the paper presents a more general framework for relating and interpreting these receptive fields conceptually and possibly predicting new receptive field profiles as well as for pre-wiring covariance under scaling, affine, and Galilean transformations into the representations of visual stimuli. This paper describes the basic structure of the necessity results concerning receptive field profiles regarding the mathematical foundation of the theory and outlines how the proposed theory could be used in further studies and modelling of biological vision. It is also shown how receptive field responses can be interpreted physically, as the superposition of relative variations of surface structure and illumination variations, given a logarithmic brightness scale, and how receptive field measurements will be invariant under multiplicative illumination variations and exposure control mechanisms. PMID:24197240
On evaluation of nonplanar diagrams in noncommutative field theory
NASA Astrophysics Data System (ADS)
Liao, Yi
2005-05-01
This is a technical work about how to evaluate loop integrals appearing in one loop nonplanar (NP) diagrams in noncommutative (NC) field theory. The conventional wisdom says that, barring the ultraviolet/infrared (UV/IR) mixing problem, NP diagrams whose planar counterparts are UV divergent are rendered finite by NC phases that couple the loop momentum to the external ones p through an NC momentum ρ=θp. We show that this is generally not the case. We find that subtleties arise already in the simpler case of Euclidean spacetime. The situation is even worse in Minkowski spacetime due to its indefinite metric. We compare different prescriptions that may be used to evaluate loop integrals in ordinary theory. They are equivalent in the sense that they always yield identical results. However, in NC theory there is no a priori reason that these prescriptions, except for the defining one that is built in the Feynman propagator, are physically justified even when they seem mathematically meaningful. Employing them can lead to ambiguous results, which are also different from those obtained according to the defining prescription. For ρ>0, the NC phase can worsen the UV property of loop integrals instead of always improving it in high dimensions. We explain how this surprising phenomenon comes about from the indefinite metric. This lends a strong support to the point of view that the naive approach is not well-founded when time does not commute with space. For ρ<0, the NC phase improves the UV property and softens the quadratic UV divergence in ordinary theory to a bounded but indefinite UV oscillation. We employ a cut-off method to quantify the new UV nonregular terms. For ρ>0, these terms are generally complex and thus also harm unitarity in addition to those found previously. As the new terms for both cases are not available in the Lagrangian and in addition can be non-Hermitian when time does not commute with space, our result casts doubts on previous demonstrations of one loop renormalizability based exclusively upon analysis of planar diagrams, especially in theories with quadratic divergences.
Saririan, K.
1997-05-01
In this thesis, the author presents some works in the direction of studying quantum effects in locally supersymmetric effective field theories that appear in the low energy limit of superstring theory. After reviewing the Kaehler covariant formulation of supergravity, he shows the calculation of the divergent one-loop contribution to the effective boson Lagrangian for supergravity, including the Yang-Mills sector and the helicity-odd operators that arise from integration over fermion fields. The only restriction is on the Yang-Mills kinetic energy normalization function, which is taken diagonal in gauge indices, as in models obtained from superstrings. He then presents the full result for the divergent one-loop contribution to the effective boson Lagrangian for supergravity coupled to chiral and Yang-Mills supermultiplets. He also considers the specific case of dilaton couplings in effective supergravity Lagrangians from superstrings, for which the one-loop result is considerably simplified. He studies gaugino condensation in the presence of an intermediate mass scale in the hidden sector. S-duality is imposed as an approximate symmetry of the effective supergravity theory. Furthermore, the author includes in the Kaehler potential the renormalization of the gauge coupling and the one-loop threshold corrections at the intermediate scale. It is shown that confinement is indeed achieved. Furthermore, a new running behavior of the dilaton arises which he attributes to S-duality. He also discusses the effects of the intermediate scale, and possible phenomenological implications of this model.
Supergauge Field Theory of Covariant Heterotic Strings
NASA Astrophysics Data System (ADS)
Kaku, M.
We present the gauge covariant second quantized field theory for free heterotic strings, which is leading candidate for a unified theory of all known particles. Our action is invariant under the semi-direct product of the super Virasoro and the Kac-Moody E_8 {times} E_8 or Spin(32)/Z_2 group. We derive th covariant action by path integrals in the same way that Feynman originally derived the Schrödinger equation. By adding an infinite number of auxiliary fields, we can also make the action explicitly local. We stress that our path integral methods can be generalized to the interacting case of splitting strings. We expect that the complete interacting theory will be a non-linear realization of the Virasoro and Kac-Moody algebras. Understanding the geometry behind such theories may eventually help in a textit{non-perturbative} formulation of the theory, in which 10 dimensional space-time is dynamically broken down to our four dimensional universe.
Inflation and deformation of conformal field theory
Garriga, Jaume; Urakawa, Yuko E-mail: yurakawa@ffn.ub.es
2013-07-01
It has recently been suggested that a strongly coupled phase of inflation may be described holographically in terms of a weakly coupled quantum field theory (QFT). Here, we explore the possibility that the wave function of an inflationary universe may be given by the partition function of a boundary QFT. We consider the case when the field theory is a small deformation of a conformal field theory (CFT), by the addition of a relevant operator O, and calculate the primordial spectrum predicted in the corresponding holographic inflation scenario. Using the Ward-Takahashi identity associated with Weyl rescalings, we derive a simple relation between correlators of the curvature perturbation ζ and correlators of the deformation operator O at the boundary. This is done without specifying the bulk theory of gravitation, so that the result would also apply to cases where the bulk dynamics is strongly coupled. We comment on the validity of the Suyama-Yamaguchi inequality, relating the bi-spectrum and tri-spectrum of the curvature perturbation.
Field theory for zero sound and ion acoustic wave in astrophysical matter
NASA Astrophysics Data System (ADS)
Gabadadze, Gregory; Rosen, Rachel A.
2016-02-01
We set up a field theory model to describe the longitudinal low-energy modes in high density matter present in white dwarf stars. At the relevant scales, ions—the nuclei of oxygen, carbon, and helium—are treated as heavy pointlike spin-0 charged particles in an effective field theory approach, while the electron dynamics is described by the Dirac Lagrangian at the one-loop level. We show that there always exists a longitudinal gapless mode in the system irrespective of whether the ions are in a plasma, crystal, or quantum liquid state. For certain values of the parameters, the gapless mode can be interpreted as a zero sound mode and, for other values, as an ion acoustic wave; we show that the zero sound and ion acoustic wave are complementary to each other. We discuss possible physical consequences of these modes for properties of white dwarfs.
Alpha particles in effective field theory
Caniu, C.
2014-11-11
Using an effective field theory for alpha (α) particles at non-relativistic energies, we calculate the strong scattering amplitude modified by Coulomb corrections for a system of two αs. For the strong interaction, we consider a momentum-dependent interaction which, in contrast to an energy dependent interaction alone [1], could be more useful in extending the theory to systems with more than two α particles. We will present preliminary results of our EFT calculations for systems with two alpha particles.
Marginal deformations of nonrelativistic field theories
NASA Astrophysics Data System (ADS)
Mallayev, Davron; Vázquez-Poritz, Justin F.; Zhang, Zhibai
2014-11-01
We construct the supergravity duals of marginal deformations of a (0, 2) Landau-Ginsburg theory that describes the supersymmetric lowest Landau level. These deformations preserve supersymmetry and it is proposed that they are associated with the introduction of a phase in the (0, 2) superpotential. We also consider marginal deformations of various field theories that exhibit Schrödinger symmetry and Lifshitz scaling. This includes countably infinite examples with dynamical exponent z =2 based on the Sasaki-Einstein spaces Yp ,q and Lp ,q ,r, as well as an example with general dynamical exponent z ≥1 .
Modified Hamiltonian formalism for higher-derivative theories
Andrzejewski, K.; Gonera, J.; Machalski, P.; Maslanka, P.
2010-08-15
An alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach, it has the following advantages: (i) The Lagrangian, when expressed in terms of new variables, yields proper equations of motion; no additional Lagrange multipliers are necessary. (ii) The Legendre transformation can be performed in a straightforward way, provided the Lagrangian is nonsingular in the Ostrogradski sense. The generalizations to singular Lagrangians as well as field theory are presented.
Hyperfunction quantum field theory: Basic structural results
NASA Astrophysics Data System (ADS)
Brüning, Erwin; Nagamachi, Shigeaki
1989-10-01
The choice of the class E' of generalized functions on space-time in which to formulate general relativistic quantum field theory (QFT) is discussed. A first step is to isolate a set of conditions on E' that allows a formulation of QFT in otherwise the same way as the original proposal by Wightman [Ark. Fys. 28, 129 (1965)], where E' is the class of tempered distributions. It is stressed that the formulation of QFT in which E' equals the class of Fourier hyperfunctions on space-time meets the following requirements: (A) Fourier hyperfunctions generalize tempered distributions thus allowing more singular fields as suggested by concrete models; (B) Fourier hyperfunction quantum fields are localizable both in space-time and in energy-momentum space thus allowing the physically indispensable standard interpretation of Poincaré covariance, local commutativity, and localization of energy-momentum spectrum; and (C) in Fourier hyperfunction quantum field theory almost all the basic structural results of ``standard'' QFT (existence of a PCT operator, spin-statistics theorems, existence of a scattering operator, etc.) hold. Finally, a short introduction to that part of Fourier hyperfunction theory needed in this context is given.
String Field Theory from Quantum Gravity
NASA Astrophysics Data System (ADS)
Crane, Louis
2013-11-01
Recent work on neutrino oscillations suggests that the three generations of fermions in the standard model are related by representations of the finite group A(4), the group of symmetries of the tetrahedron. Motivated by this, we explore models which extend the EPRL model for quantum gravity by coupling it to a bosonic quantum field of representations of A(4). This coupling is possible because the representation category of A(4) is a module category over the representation categories used to construct the EPRL model. The vertex operators which interchange vacua in the resulting quantum field theory reproduce the bosons and fermions of the standard model, up to issues of symmetry breaking which we do not resolve. We are led to the hypothesis that physical particles in nature represent vacuum changing operators on a sea of invisible excitations which are only observable in the A(4) representation labels which govern the horizontal symmetry revealed in neutrino oscillations. The quantum field theory of the A(4) representations is just the dual model on the extended lattice of the Lie group E6, as explained by the quantum McKay correspondence of Frenkel, Jing and Wang. The coupled model can be thought of as string field theory, but propagating on a discretized quantum spacetime rather than a classical manifold.
Noether symmetries, energy-momentum tensors, and conformal invariance in classical field theory
Pons, Josep M.
2011-01-15
In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. With this baggage on board, we next discuss in detail, for Poincare invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of Poincare symmetries and it is a basic ingredient of the generators of other eventual spacetime symmetries which may happen to exist. Instead, Hilbert tensors are the means to test whether a theory contains other spacetime symmetries beyond Poincare. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincare invariant Lagrangians, that the realization of scale invariance selects a unique Hilbert tensor which allows for an easy test as to whether conformal invariance is also realized. Finally we make some basic remarks on metric generally covariant theories and classical field theory in a fixed curved background.
Vortex operators in gauge field theories
Polchinski, J.
1980-07-01
Several related aspects of the 't Hooft vortex operator are studied. The current picture of the vacuum of quantum chromodynamics, the idea of dual field theories, and the idea of the vortex operator are reviewed first. The Abelian vortex operator written in terms of elementary fields and the calculation of its Green's functions are considered. A two-dimensional solvable model of a Dirac string is presented. The expression of the Green's functions more neatly in terms of Wu and Yang's geometrical idea of sections is addressed. The renormalization of the Green's functions of two kinds of Abelian looplike operators, the Wilson loop and the vortex operator, is studied; for both operators only an overall multiplicative renormalization is needed. In the case of the vortex this involves a surprising cancellation. Next, the dependence of the Green's functions of the Wilson and 't Hooft operators on the nature of the vacuum is discussed. The cluster properties of the Green's functions are emphasized. It is seen that the vortex operator in a massive Abelian theory always has surface-like clustering. The form of Green's functions in terms of Feynman graphs is the same in Higgs and symmetric phases; the difference appears in the sum over all tadpole trees. Finally, systems having fields in the fundamental representation are considered. When these fields enter only weakly into the dynamics, a vortex-like operator is anticipated. Any such operator can no longer be local looplike, but must have commutators at long range. A U(1) lattice gauge theory with two matter fields, one singly charged (fundamental) and one doubly charged (adjoint), is examined. When the fundamental field is weakly coupled, the expected phase transitions are found. When it is strongly coupled, the operator still appears to be a good order parameter, a discontinuous change in its behavior leads to a new phase transition. 18 figures.
Gravity duals for nonrelativistic conformal field theories.
Balasubramanian, Koushik; McGreevy, John
2008-08-01
We attempt to generalize the anti-de Sitter/conformal field theory correspondence to nonrelativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and, more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with a negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and find two-point correlators of the correct form. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions. PMID:18764448
Quantum algorithms for quantum field theories
NASA Astrophysics Data System (ADS)
Jordan, Stephen
2015-03-01
Ever since Feynman's original proposal for quantum computers, one of the primary applications envisioned has been efficient simulation of other quantum systems. In fact, it has been conjectured that quantum computers would be universal simulators, which can simulate all physical systems using computational resources that scale polynomially with the system's number of degrees of freedom. Quantum field theories have posed a challenge in that the set of degrees of freedom is formally infinite. We show how quantum computers, if built, could nevertheless efficiently simulate certain quantum field theories at bounded energy scales. Our algorithm includes a new state preparation technique which we believe may find additional applications in quantum algorithms. Joint work with Keith Lee and John Preskill.
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Quantitative field theory of the glass transition
Franz, Silvio; Jacquin, Hugo; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco
2012-01-01
We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature, we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we analytically study the critical behavior of a set of four-points correlation functions, from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the hypernetted chain approximation for the Gibbs free energy, and we find results that are consistent with numerical simulations. PMID:23112202
Effective Field Theory for Lattice Nuclei
NASA Astrophysics Data System (ADS)
Barnea, N.; Contessi, L.; Gazit, D.; Pederiva, F.; van Kolck, U.
2015-02-01
We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. We argue that pionless EFT is the appropriate theory to describe the light nuclei obtained in LQCD simulations carried out at pion masses heavier than the physical pion mass. We solve the EFT using the effective-interaction hyperspherical harmonics and auxiliary-field diffusion Monte Carlo methods. Fitting the three leading-order EFT parameters to the deuteron, dineutron, and triton LQCD energies at mπ≈800 MeV , we reproduce the corresponding alpha-particle binding and predict the binding energies of mass-5 and mass-6 ground states.
Probabilities and signalling in quantum field theory
NASA Astrophysics Data System (ADS)
Dickinson, Robert; Forshaw, Jeff; Millington, Peter
2016-03-01
We present an approach to computing probabilities in quantum field theory for a wide class of source-detector models. The approach works directly with probabilities and not with squared matrix elements, and the resulting probabilities can be written in terms of expectation values of nested commutators and anticommutators. We present results that help in the evaluation of these, including an expression for the vacuum expectation values of general nestings of commutators and anticommutators in scalar field theory. This approach allows one to see clearly how faster-than-light signalling is prevented, because it leads to a diagrammatic expansion in which the retarded propagator plays a prominent role. We illustrate the formalism using the simple case of the much-studied Fermi two-atom problem.
Superconformal quantum field theory in curved spacetime
NASA Astrophysics Data System (ADS)
de Medeiros, Paul; Hollands, Stefan
2013-09-01
By conformally coupling vector and hyper multiplets in Minkowski space, we obtain a class of field theories with extended rigid conformal supersymmetry on any Lorentzian 4-manifold admitting twistor spinors. We construct the conformal symmetry superalgebras which describe classical symmetries of these theories and derive an appropriate BRST operator in curved spacetime. In the process, we elucidate the general framework of cohomological algebra which underpins the construction. We then consider the corresponding perturbative quantum field theories. In particular, we examine the conditions necessary for conformal supersymmetries to be preserved at the quantum level, i.e. when the BRST operator commutes with the perturbatively defined S-matrix, which ensures superconformal invariance of amplitudes. To this end, we prescribe a renormalization scheme for time-ordered products that enter the perturbative S-matrix and show that such products obey certain Ward identities in curved spacetime. These identities allow us to recast the problem in terms of the cohomology of the BRST operator. Through a careful analysis of this cohomology, and of the renormalization group in curved spacetime, we establish precise criteria which ensure that all conformal supersymmetries are preserved at the quantum level. As a by-product, we provide a rigorous proof that the beta-function for such theories is one-loop exact. We also briefly discuss the construction of chiral rings and the role of non-perturbative effects in curved spacetime.
Entanglement entropy in scalar field theory
NASA Astrophysics Data System (ADS)
Hertzberg, Mark P.
2013-01-01
Understanding the dependence of entanglement entropy on the renormalized mass in quantum field theories can provide insight into phenomena such as quantum phase transitions, since the mass varies in a singular way near the transition. Here we perturbatively calculate the entanglement entropy in interacting scalar field theory, focusing on the dependence on the field’s mass. We study λϕ4 and gϕ3 theories in their ground state. By tracing over a half space, using the replica trick and position space Green’s functions on the cone, we show that spacetime volume divergences cancel and renormalization can be consistently performed in this conical geometry. We establish finite contributions to the entanglement entropy up to two-loop order, involving a finite area law. The resulting entropy is simple and intuitive: the free theory result in d = 3 (that we included in an earlier publication) ΔS ˜ A m2ln (m2) is altered, to leading order, by replacing the bare mass m by the renormalized mass mr evaluated at the renormalization scale of zero momentum.
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean
NASA Astrophysics Data System (ADS)
Beron-Vera, Francisco J.; Olascoaga, María J.; Haller, George; Farazmand, Mohammad; Triñanes, Joaquín; Wang, Yan
2015-08-01
Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean.
Beron-Vera, Francisco J; Olascoaga, María J; Haller, George; Farazmand, Mohammad; Triñanes, Joaquín; Wang, Yan
2015-08-01
Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions. PMID:26328583
Simulating quantum field theories with superconducting circuits
NASA Astrophysics Data System (ADS)
Romero, Guillermo; García-Álvarez, Laura; Casanova, Jorge; Mezzacapo, Antonio; Lamata, Lucas; Solano, Enrique
2014-03-01
In this contribution, we present the quantum simulation of fermionic field modes interacting via a continuum of bosonic modes with superconducting circuits. Unlike many quantum technologies, superconducting circuits offer naturally the continuum of bosonic modes by means of one-dimensional transmission lines. In particular, we consider a simplified version of 1+1 quantum electrodynamics (QED), which may describe Yukawa interactions, and the coupling of fermions to the Higgs field. Our proof-of-principle proposal is designed within the state-of-the-art circuit QED technology, where fermionic fields are encoded in superconducting flux qubits, in a scalable approach that may lead to a full-fledged quantum simulation of quantum field theories. The author acknowledge support from Spanish MINECO FIS2012-36673-C03-02; UPV/EHU UFI 11/55; Basque Government IT472-10; SOLID, CCQED, PROMISCE, and SCALEQIT European projects.
Complete action for open superstring field theory
NASA Astrophysics Data System (ADS)
Kunitomo, Hiroshi; Okawa, Yuji
2016-02-01
We construct a complete action for open superstring field theory that includes the Neveu-Schwarz sector and the Ramond sector. For the Neveu-Schwarz sector, we use the string field in the large Hilbert space of the superconformal ghost sector, and the action in the Neveu-Schwarz sector is the same as the Wess-Zumino-Witten-like action of the Berkovits formulation. For the Ramond sector, it is known that the BRST cohomology on an appropriate subspace of the small Hilbert space reproduces the correct spectrum, and we use the string field projected to this subspace. We show that the action is invariant under gauge transformations that are consistent with the projection for the string field in the Ramond sector.
Advances in String Field Theory (Abstract)
Schnabl, M.
2007-10-03
In this talk we have reviewed basics of Witten's open string field theory. We have described tools that allow one to construct a solution of the classical equations of motion describing the tachyon vacuum, and to prove two of the Sen's conjectures. Discussion of background independence and related issue of representing marginal deformations of the underlying CFT was also given. Finally some preliminary results hinting at existence of solutions describing multiple space-filling D-branes were presented.
Capture Reactions with Halo Effective Field Theory
NASA Astrophysics Data System (ADS)
Higa, R.
2015-12-01
Loosely bound nuclei far from the stability region emerge as a quantum phenomenon with many universal properties. The connection between these properties and the underlying symmetries can be best explored with halo/cluster EFT, an effective field theory where the softness of the binding momentum and the hardness of the core(s) form the expansion parameter of a given perturbative approach. In the following I highlight a particular application where these ideas are being tested, namely capture reactions.
Halo Effective Field Theory of 6He
NASA Astrophysics Data System (ADS)
Thapaliya, Arbin; Ji, Chen; Phillips, Daniel
2016-03-01
6He has a cluster structure with a tight 4He (α) core surrounded by two loosely bound neutrons (n) making it a halo nucleus. The leading-order (LO) Halo Effective Field Theory (EFT) [1, 2] calculations using momentum-space Faddeev equations pertinent to a bound 6He were carried out in [3]. In this work, we investigate 6He up to next-to-leading order (NLO) within Halo EFT.
Superconformal partial waves in Grassmannian field theories
NASA Astrophysics Data System (ADS)
Doobary, Reza; Heslop, Paul
2015-12-01
We derive superconformal partial waves for all scalar four-point functions on a super Grassmannian space Gr( m| n, 2 m|2 n) for all m, n. This family of four-point functions includes those of all (arbitrary weight) half BPS operators in both N=4 SYM ( m = n = 2) and in N = 2 superconformal field theories in four dimensions ( m = 2 , n = 1) on analytic superspace. It also includes four-point functions of all (arbitrary dimension) scalar fields in non-supersymmetric conformal field theories ( m = 2 , n = 0) on Minkowski space, as well as those of a certain class of representations of the compact SU(2 n) coset spaces. As an application we then specialise to N=4 SYM and use these results to perform a detailed superconformal partial wave analysis of the four-point functions of arbitrary weight half BPS operators. We discuss the non-trivial separation of protected and unprotected sectors for the <2222>, <2233> and <3333> cases in an SU( N) gauge theory at finite N. The <2233> correlator predicts a non-trivial protected twist four sector for <3333> which we can completely determine using the knowledge that there is precisely one such protected twist four operator for each spin.
Perturbation theory, effective field theory, and oscillations in the power spectrum
NASA Astrophysics Data System (ADS)
Vlah, Zvonimir; Seljak, Uroš; Yat Chu, Man; Feng, Yu
2016-03-01
We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the results of effective field theory (EFT), and can thus be expanded in terms of the same parameters. We find that its radius of convergence is larger than the SPT loop expansion. The same EFT parametrization applies to all SPT loop terms and if stochasticity can be ignored, to all N-point correlators. In 3-d, the LPT structure is considerably more complicated, and we find that LPT models with parametrization motivated by the EFT exhibit running with k and that SPT is generally a better choice. Since these transfer function expansions contain free parameters that change with cosmological model their usefulness for broadband power is unclear. For this reason we test the predictions of these models on baryonic acoustic oscillations (BAO) and other primordial oscillations, including string monodromy models, for which we ran a series of simulations with and without oscillations. Most models are successful in predicting oscillations beyond their corresponding PT versions, confirming the basic validity of the model. We show that if primordial oscillations are localized to a scale q, the wiggles in power spectrum are approximately suppressed as exp[-k2Σ2(q)/2], where Σ(q) is rms displacement of particles separated by q, which saturates on large scales, and decreases as q is reduced. No oscillatory features survive past k ~ 0.5h/Mpc at z = 0.
Galvao, C.A.; Nutku, Y.
1996-12-01
mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}
Scalar Field Theories with Polynomial Shift Symmetries
NASA Astrophysics Data System (ADS)
Griffin, Tom; Grosvenor, Kevin T.; Hořava, Petr; Yan, Ziqi
2015-12-01
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree P in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree P, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree P? To answer this (essentially cohomological) question, we develop a new graph-theoretical technique, and use it to prove several classification theorems. First, in the special case of P = 1 (essentially equivalent to Galileons), we reproduce the known Galileon N-point invariants, and find their novel interpretation in terms of graph theory, as an equal-weight sum over all labeled trees with N vertices. Then we extend the classification to P > 1 and find a whole host of new invariants, including those that represent the most relevant (or least irrelevant) deformations of the corresponding Gaussian fixed points, and we study their uniqueness.
NASA Astrophysics Data System (ADS)
Destouni, G.; Cvetkovic, V.; Selroos, J.-O.; Persson, K.; Jarsjo, J.
2012-04-01
This paper presents how tracer, nutrient and pollutant transport through a catchment can be analyzed based on mean flow and other flow-transport properties given or resolved by simulations, by following the trajectories (pathways) of transport through the catchment and the flow-transport property distribution among them. Convolution of relevant property distributions across consecutive hydrological units, aggregated over the trajectories that originate from the tracer/pollutant-specific injection area, captures hydrological dispersion with its basic measure derived as the travel time coefficient of variation. Various memory functions can be introduced in a relatively simple manner for incorporating retention/mass transfer mechanisms under conditions of statistical stationarity. The paper further shows how spatial and temporal flow variability can be accounted for in this general theory, and how each and both of these variability components influence hydrological transport in catchments. Moreover, the paper outlines how the theory can be used in a scenario analysis approach to quantify and map the effects of uncertainty in physical and biogeochemical characteristics on diffuse hydrological transport and its uncertainty.
Yangian superalgebras in conformal field theory
NASA Astrophysics Data System (ADS)
Creutzig, Thomas
2011-08-01
Quantum Yangian symmetry in several sigma models with supergroup or supercoset as target is established. Starting with a two-dimensional conformal field theory that has current symmetry of a Lie superalgebra with vanishing Killing form we construct non-local charges and compute their properties. Yangian axioms are satisfied, except that the Serre relations only hold for a subsector of the space of fields. Yangian symmetry implies that correlation functions of fields in this sector satisfy Ward identities. We then show that this symmetry is preserved by certain perturbations of the conformal field theory. The main examples are sigma models of the supergroups PSL(N|N), OSP(2N+2|2N) and D(2,1;α) away from the WZW point. Further there are the OSP(2N+2|2N) Gross-Neveu models and current-current perturbations of ghost systems, both for the disc as world-sheet. The latter we show to be equivalent to CP sigma models, while the former are conjecturally dual to supersphere sigma models.
Gravitational Goldstone fields from affine gauge theory
NASA Astrophysics Data System (ADS)
Tresguerres, Romualdo; Mielke, Eckehard W.
2000-08-01
In order to facilitate the application of standard renormalization techniques, gravitation should be described, in the pure connection formalism, as a Yang-Mills theory of a certain spacetime group, say the Poincaré or the affine group. This embodies the translational as well as the linear connection. However, the coframe is not the standard Yang-Mills-type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring this ``hidden'' piece within the framework of nonlinear realizations, the usual geometrical interpretation of the dynamical theory becomes possible, and in addition one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. We claim that nonlinear realizations provide the general mathematical scheme for the foundation of gauge theories of spacetime symmetries. When applied to construct the Yang-Mills theory of the affine group, tetrads become identified with nonlinear translational connections; the anholonomic metric no longer constitutes an independent gravitational potential, since its degrees of freedom reveal a correspondence to eliminateable Goldstone bosons. This may be an important advantage for quantization.
Dynamic field theory and equations of motion in cosmology
Kopeikin, Sergei M.; Petrov, Alexander N.
2014-11-15
We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ≫1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress–energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein’s equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.
Dynamic field theory and equations of motion in cosmology
NASA Astrophysics Data System (ADS)
Kopeikin, Sergei M.; Petrov, Alexander N.
2014-11-01
We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein's equations in the form of the Friedmann-Lemaître-Robertson-Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ / ρ ≤ 1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ / ρ ≫ 1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress-energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein's equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.
Working Group Report: Lattice Field Theory
Blum, T.; et al.,
2013-10-22
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
Theory of field-reversed configurations
NASA Astrophysics Data System (ADS)
Steinhauer, L. C.
1993-01-01
This report summarizes results from the theoretical program on field reversed configurations (FRC) at STI Optronics. The program, which has spanned the last 13 years, has included analytical as well as computational components. It has led to published papers on every major topic of FRC theory. The report is outlined to summarize results from each of these topic areas: formation, equilibrium, stability, and confinement. Also briefly described are Steinhauer's activities as Compact Toroid Theory Listening Post. Appendix A is a brief listing of the major advances achieved in this program. Attached at the back of this report is a collection of technical papers in archival journals that resulted from work in this program. The discussion within each subsection is given chronologically in order to give a historical sense of the evolution of understanding of FRC physics.
A novel string field theory solving string theory by liberating left and right movers
NASA Astrophysics Data System (ADS)
Nielsen, Holger B.; Ninomiya, Masao
2014-05-01
We put forward ideas to a novel string field theory based on making some "objects" that essentially describe "liberated" left- and right- mover fields ( τ + σ) and ( τ - σ) on the string. Our novel string field theory is completely definitely different from any other string theory in as far as a "null set" of information in the string field theory Fock space has been removed relatively, to the usual string field theories. So our theory is definitely new. The main progress is that we manage to make our novel string field theory provide the correct mass square spectrum for the string. We finally suggest how to obtain the Veneziano amplitude in our model.
The effective field theory of dark energy
Gubitosi, Giulia; Vernizzi, Filippo; Piazza, Federico E-mail: fpiazza@apc.univ-paris7.fr
2013-02-01
We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar can always be de-mixed from gravity at quadratic order in the perturbations, but not necessarily through a conformal rescaling of the metric. We show how to express covariant field-operators in our formalism and give several explicit examples of dark energy and modified gravity models in our language. Finally, we discuss the relation with the covariant EFT methods recently appeared in the literature.
Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
NASA Astrophysics Data System (ADS)
Tolotti, Mathias; Weinzierl, Stefan
2013-07-01
The BCJ decomposition is a highly non-trivial property of gauge theories. In this paper we systematically construct an effective Lagrangian, whose Feynman rules automatically produce the BCJ numerators. The effective Lagrangian contains non-local terms. The difference between the standard Yang-Mills Lagrangian and the effective Lagrangian simplifies to zero.
Temperature Gradient Field Theory of Nucleation
NASA Astrophysics Data System (ADS)
Das, S.; Ain, W. Q.; Azhari, A.; Prasada Rao, A. K.
2016-02-01
According to the proposed theory, ceramic particles present in molten metal, lose heat at a slower rate than the metallic liquid during cooling. Such condition results in the formation of a spherical thermal gradient field (TGF) around each particle. Hence, the interstitials (low temperature) of such TGFs are the regions to reach the nucleation temperature first, owing to low energy barrier than the liquid-particle interface (higher temperature). Analytics also indicate that the nucleation rate is higher at the TGF interstitials, than at the liquid-particle interface. Such TGF network results in simultaneous nucleation throughout the system, resulting in grain refinement.
Theory of microemulsions in a gravitational field
NASA Technical Reports Server (NTRS)
Jeng, J. F.; Miller, Clarence A.
1989-01-01
A theory of microemulsions developed previously is extended to include the effect of a gravitational field. It predicts variation with position of drop size, drop volume fraction, and area per molecule in the surfactant films within a microemulsion phase. Variation in volume fraction is greatest and occurs in such a way that oil content increases with increasing elevation, as has been found experimentally. Large composition variations are predicted within a middle phase microemulsion near optimal conditions because inversion from the water-continuous to the oil-continuous arrangement occurs with increasing elevation. Generally speaking, gravity reduces solubilization within microemulsions and promotes separation of excess phases.
Scalar-field theory of dark matter
NASA Astrophysics Data System (ADS)
Huang, Kerson; Xiong, Chi; Zhao, Xiaofei
2014-05-01
We develop a theory of dark matter based on a previously proposed picture, in which a complex vacuum scalar field makes the universe a superfluid, with the energy density of the superfluid giving rise to dark energy, and variations from vacuum density giving rise to dark matter. We formulate a nonlinear Klein-Gordon equation to describe the superfluid, treating galaxies as external sources. We study the response of the superfluid to the galaxies, in particular, the emergence of the dark-matter galactic halo, contortions during galaxy collisions and the creation of vortices due to galactic rotation.
Purely cubic action for string field theory
NASA Technical Reports Server (NTRS)
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
Drift estimation from a simple field theory
Mendes, F. M.; Figueiredo, A.
2008-11-06
Given the outcome of a Wiener process, what can be said about the drift and diffusion coefficients? If the process is stationary, these coefficients are related to the mean and variance of the position displacements distribution. However, if either drift or diffusion are time-dependent, very little can be said unless some assumption about that dependency is made. In Bayesian statistics, this should be translated into some specific prior probability. We use Bayes rule to estimate these coefficients from a single trajectory. This defines a simple, and analytically tractable, field theory.
Point-form quantum field theory
Biernat, E.P. Klink, W.H. Schweiger, W. Zelzer, S.
2008-06-15
We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form x{sub {mu}}x{sup {mu}} = {tau}{sup 2}. This choice of quantization surface implies that all components of the 4-momentum operator are affected by interactions (if present), whereas rotation and boost generators remain interaction free-a feature characteristic of Dirac's 'point-form' of relativistic dynamics. Unlike previous attempts to quantize fields on space-time hyperboloids, we keep the usual plane-wave expansion of the field operators and consider evolution of the system generated by the 4-momentum operator. We verify that the Fock-space representations of the Poincare generators for free scalar and spin-1/2 fields look the same as for equal-time quantization. Scattering is formulated for interacting fields in a covariant interaction picture and it is shown that the familiar perturbative expansion of the S-operator is recovered by our approach. An appendix analyzes special distributions, integrals over the forward hyperboloid, that are used repeatedly in the paper.
Local superfield Lagrangian BRST quantization
NASA Astrophysics Data System (ADS)
Gitman, D. M.; Moshin, P. Yu.; Reshetnyak, A. A.
2005-07-01
A θ-local formulation of superfield Lagrangian quantization in non-Abelian hypergauges is proposed on the basis of an extension of general reducible gauge theories to special superfield models with a Grassmann parameter θ. We solve the problem of describing the quantum action and the gauge algebra of an L-stage-reducible superfield model in terms of a BRST charge for a formal dynamical system with first-class constraints of (L+1)-stage reducibility. Starting from θ-local functions of the quantum and gauge-fixing actions, with an essential use of Darboux coordinates on the antisymplectic manifold, we construct a superfield generating functionals of Green's functions, including the effective action. We present two superfield forms of BRST transformations, considered as θ-shifts along vector fields defined by Hamiltonian-like systems constructed in terms of the quantum and gauge-fixing actions and an arbitrary θ-local boson function, as well as in terms of corresponding fermion functionals, through Poisson brackets with opposite Grassmann parities. The gauge independence of the S-matrix is proved. The Ward identities are derived. Connection is established with the BV method, the multilevel Batalin-Tyutin formalism, as well as with the superfield quantization scheme of Lavrov, Moshin, and Reshetnyak, extended to the case of general coordinates.
Towards a quantum field theory of primitive string fields
Ruehl, W.
2012-10-15
We denote generating functions of massless even higher-spin fields 'primitive string fields' (PSF's). In an introduction we present the necessary definitions and derive propagators and currents of these PDF's on flat space. Their off-shell cubic interaction can be derived after all off-shell cubic interactions of triplets of higher-spin fields have become known. Then we discuss four-point functions of any quartet of PSF's. In subsequent sections we exploit the fact that higher-spin field theories in AdS{sub d+1} are determined by AdS/CFT correspondence from universality classes of critical systems in d-dimensional flat spaces. The O(N) invariant sectors of the O(N) vector models for 1 {<=} N {<=}{infinity} play for us the role of 'standard models', for varying N, they contain, e.g., the Ising model for N = 1 and the spherical model for N = {infinity}. A formula for the masses squared that break gauge symmetry for these O(N) classes is presented for d = 3. For the PSF on AdS space it is shown that it can be derived by lifting the PSF on flat space by a simple kernel which contains the sum over all spins. Finally we use an algorithm to derive all symmetric tensor higher-spin fields. They arise from monomials of scalar fields by derivation and selection of conformal (quasiprimary) fields. Typically one monomial produces a multiplet of spin s conformal higher-spin fields for all s {>=} 4, they are distinguished by their anomalous dimensions (in CFT{sub 3}) or by theirmass (in AdS{sub 4}). We sum over these multiplets and the spins to obtain 'string type fields', one for each such monomial.
Causality Is Inconsistent With Quantum Field Theory
Wolf, Fred Alan
2011-11-29
Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts non-vanishing probabilities for both negative energy particles in the forward-through-time direction and positive energy antiparticles in the backwards-through-time direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.
NASA Astrophysics Data System (ADS)
Ide, K.; Jones, C. K.
2004-12-01
Various manifestations of Lagrangian dynamics exist in the geophysical systems and their signatures may arise in distinct forms at a wide range of spatial scales. Capturing these Lagrangian signatures helps us enhance our predictive capability using the Eulerian model. In the macroscopic form, the Lagrangian signatures may be visible as coherent structures in the sequence of Eulerian synoptic fields. They are dynamically active and often identified as the regions of conserved properties with sharp gradients along the boundaries. These boundaries may be dynamically less active but are important because they govern the mixing process between the interior and exterior. In the microscopic form, the Lagrangian signature is manifest in the trajectory of a traceable marker which can be an observation instrument. The primary attributes of Lagrangian information obtained by the instruments are the ability to trace large-scale coherent structures on one hand and display small-scale mixing process on the other hand, while satisfying the conservation laws for many observed properties the along the trajectory. Lagrangian information thus offers unique perspectives of the circulation. We develop a comprehensive data assimilation platform with a focus on estimation of coherent structures in the Eulerian model through assimilation of Lagrangian data. Recent developments in the use of dynamical systems theory have brought a new aspect of Lagrangian analysis to the geophysical flow dynamics. It offers an algorithm to detect the unseen boundaries of the coherent structures as a non-local material curves originating from the relevant hyperbolic trajectories. Our data assimilation platform takes advantage of the dynamical systems theory. Targeting these hyperbolic trajectories naturally leads to an adaptive observing system.
Continuum regularization of quantum field theory
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
Classical and quantum theory of the massive spin-two field
NASA Astrophysics Data System (ADS)
Koenigstein, Adrian; Giacosa, Francesco; Rischke, Dirk H.
2016-05-01
In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark-antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers JPC =2-+ is, to our knowledge, given here for the first time.
Some mathematical aspects of quantum field theory
NASA Astrophysics Data System (ADS)
Chen, Qingtao
In recent years, physics especially Quantum Field Theory has had an enormous impact in mathematics. This thesis mainly contains two different parts of mathematical developments of problems inspired from physics. Firstly, I study Topological Quantum Field Theory and its related topics. Gromov-Witten theory of resolved conifold corresponds to the Chern-Simons theory of unknot. In a series of papers, Labastida, Marino, Ooguri, Vafa, proposed a conjectural description of Chern-Simons theory of special linear quantum group invariants of links. LMOV conjecture could be viewed as a counterpart of Gopakumar-Vafa conjecture. These are actually parts of the big picture, large N Chern-Simons/Topological string duality. In the first chapter of this part, the orthogonal quantum group version of LMOV conjecture is rigorously formulated in mathematics by using the representation of Brauer centralizer algebra. We also obtain formulae of Lichorish-Millet type which could be viewed as the application in knot theory and topology. By using the cabling technique, we obtain a uniform formula of colored Kauffman polynomial for all torus links with all partitions. Combined these together, we are able to prove many interesting cases of this orthogonal LMOV conjecture. In particular we can apply this uniform formula to verify certain case of the conjecture at roots of unity. In fact, these integer coefficients appeared in the original (orthogonal) LMOV conjecture are called the BPS numbers in string theory. In the second chapter of this part, graphic representations of the universal R-matrices has been used to discover the recursion formulae between various quantum group invariants. We study the recursion relations of R-matrices corresponding to the inclusions Uq( sln) ⊂ Uq(sl n+1), Uq(sl k) x Uq(sln--k ) ⊂ Uq(sln), Uq(sln) ⊂ U q(so2n), Uq(so2k) x Uq(sln--k) ⊂ Uq(so2n). As an application, we find the ODE recursion formulae for HOMFLY and Kauffman polynomials. Secondly, I study the Modular Forms in Topology, Elliptic Genera, Loop Space and String Manifolds. In a series of papers, the following results are discovered. By developing modular invariance on certain characteristic forms, several cancellation formulas emerge naturally as the generalization of the original gravity anomaly cancellation formulas obtained by L. Alvarez-Gaume and E. Witten in their celebrated paper [2] studying the string theory. These cancellation formulae directly imply the divisibility and the congruence phenomena of characteristic numbers by Atiyah-Singer Index theorem, which plays important roles both in topology and differential geometry. We recover the Hirzebruch divisibility of twist signature and obtain the twist higher Rokhlin congruence by applying the modular invariance properties on the elliptic forms and also prove that it is best possible by studying examples constructed from K3-surface and Bott manifold. We also obtain the divisibility results for the index of double twist signature operators. By studying the "modular transgression" on elliptic forms, we obtain some modularly invariant secondary characteristic forms on odd dimensional manifolds. Also, by using this method, we heuristically calculate the Chern-Simons forms for flat bundles over free loop space. This direction is pioneered by Witten [94), who heuristically interpreted the Landweber-Stong elliptic genus as the index of the formal signature operator on free loop space as well as introduced the formal equivariant index of the Dirac operator on loop space, known as Witten operator. We call a manifold to be string if its loop space is spin. It's known that a string manifold is a spin manifold with vanishing half first Pontryagin class. Using the arithmetic properties of Jacobi-Theta functions, we prove the vanishing of the Witten genus of certain nonsingular string complete intersections in products of complex projective spaces, which generalizes a known result of Landweber and Stong [54].
The effective field theory treatment of quantum gravity
Donoghue, John F.
2012-09-24
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.
Effective field theory for spacetime symmetry breaking
NASA Astrophysics Data System (ADS)
Hidaka, Yoshimasa; Noumi, Toshifumi; Shiu, Gary
2015-08-01
We discuss the effective field theory for spacetime symmetry breaking from the local symmetry point of view. By gauging spacetime symmetries, the identification of Nambu-Goldstone (NG) fields and the construction of the effective action are performed based on the breaking pattern of diffeomorphism, local Lorentz, and (an)isotropic Weyl symmetries as well as the internal symmetries including possible central extensions in nonrelativistic systems. Such a local picture distinguishes, e.g., whether the symmetry breaking condensations have spins and provides a correct identification of the physical NG fields, while the standard coset construction based on global symmetry breaking does not. We illustrate that the local picture becomes important in particular when we take into account massive modes associated with symmetry breaking, the masses of which are not necessarily high. We also revisit the coset construction for spacetime symmetry breaking. Based on the relation between the Maurer-Cartan one form and connections for spacetime symmetries, we classify the physical meanings of the inverse-Higgs constraints by the coordinate dimension of broken symmetries. Inverse Higgs constraints for spacetime symmetries with a higher dimension remove the redundant NG fields, whereas those for dimensionless symmetries can be further classified by the local symmetry breaking pattern.
Energy-momentum conservation laws in Finsler/Kawaguchi Lagrangian formulation
NASA Astrophysics Data System (ADS)
Ootsuka, Takayoshi; Yahagi, Ryoko; Ishida, Muneyuki; Tanaka, Erico
2015-08-01
We reformulate the standard Lagrangian formulation to a reparameterization invariant Lagrangian formulation by means of Finsler and Kawaguchi geometry. In our formulation, various types of symmetries that appear in theories of physics are expressed geometrically by symmetries of the Finsler (Kawaguchi) metric, and the conservation laws of energy momentum arise as a part of the Euler-Lagrange equations. The Euler-Lagrange equations are given geometrically in reparameterization invariant form, and the conserved energy-momentum currents can be obtained more easily than by the conventional Lagrangian formulation. The applications to scalar field, Dirac field, electromagnetic field and general relativity are introduced. In particular, we propose an alternative definition of the energy-momentum current of gravity, which satisfies gauge invariance under on-shell conditions.
LanHEP—a package for the automatic generation of Feynman rules in field theory. Version 3.0
NASA Astrophysics Data System (ADS)
Semenov, A. V.
2009-03-01
The LanHEP program version 3.0 for Feynman rules generation from the Lagrangian is described. It reads the Lagrangian written in a compact form, close to the one used in publications. It means that Lagrangian terms can be written with summation over indices of broken symmetries and using special symbols for complicated expressions, such as covariant derivative and strength tensor for gauge fields. Supersymmetric theories can be described using the superpotential formalism and the 2-component fermion notation. The output is Feynman rules in terms of physical fields and independent parameters in the form of CompHEP model files, which allows one to start calculations of processes in the new physical model. Alternatively, Feynman rules can be generated in FeynArts format or as LaTeX table. One-loop counterterms can be generated in FeynArts format. Program summaryProgram title: LanHEP Catalogue identifier: ADZV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 83 041 No. of bytes in distributed program, including test data, etc.: 1 090 931 Distribution format: tar.gz Programming language: C Computer: PC Operating system: Linux RAM: 2 MB (SM), 12 MB (MSSM), 120 MB (MSSM with counterterms) Classification: 4.4 Nature of problem: Deriving Feynman rules from the Lagrangian Solution method: The program reads the Lagrangian written in a compact form, close to the one used in publications. It means that Lagrangian terms can be written with summation over indices of broken symmetries and using special symbols for complicated expressions, such as covariant derivative and strength tensor for gauge fields. Tools for checking the correctness of the model, and for simplifying the output expressions are provided. The output is Feynman rules in terms of physical fields and independent parameters in the form of CompHEP model files, which allows one to start calculations of processes in the new physical model. Alternatively, Feynman rules can be generated in FeynArts format or as a LaTeX table. Running time: 1 sec (SM), 8 sec (MSSM), 8 min (MSSM with counterterms)
Alternative Expression for the Electromagnetic Lagrangian
NASA Astrophysics Data System (ADS)
Saldanha, Pablo L.
2016-04-01
We reintroduce an alternative expression for the Lagrangian density that governs the interaction of a charged particle with external electromagnetic fields, proposed by Livens about one century ago. This Lagrangian is written in terms of the local superposition of the particle fields with the applied electromagnetic fields, not in terms of the particle charge and of the electromagnetic potentials as is usual. Here, we show that the total Lagrangian for a set of charged particles assumes a simple elegant form with the alternative formulation, giving an aesthetic support for it. We also show that the alternative Lagrangian is equivalent to the traditional one in their domain of validity and that it provides an interesting description of the Aharonov-Bohm effect.
Effective field theory analysis of Higgs naturalness
Bar-Shalom, Shaouly; Soni, Amarjit; Wudka, Jose
2015-07-20
Assuming the presence of physics beyond the Standard Model ( SM) with a characteristic scale M ~ O (10) TeV, we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the leading 1 -loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff, and determine t he constraints on the corresponding operator coefficients for these effects to alleviate the little hierarchy problem up to the scale of the effective action Λ < M , a condition we denote by “EFT-naturalness”. We also determine the types of physics that can lead to EFT-naturalness and show that these types of new physics are best probed in vector-boson and multiple-Higgs production. The current experimental constraints on these coefficients are also discussed.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2014-08-29
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field. PMID:25215973
Integrable Conformal Field Theory - A Case Study
Schomerus, Volker
2010-06-17
Over the last decades, 2-dimensional conformal field theory has been developed into a powerful tool that has been applied to problems in diverse branches of physics and mathematics. Models are usually solved algebraically by exploiting certain infinite dimensional symmetries. But the presence of sufficient world-sheet symmetry is a rather exceptional feature, one that is e.g. not present for curved string backgrounds at generic points in moduli space. In this note I review some recent work which aims at computing spectra of conformal sigma models without spectrum generating symmetries. Our main results are illustrated at the example of complex projective superspace (C) P{sup N-1|N}. This note is based on several publications with C. Candu, T. Creutzig, V. Mitev, T. Quella and H. Saleur.
Standard Model as a Double Field Theory.
Choi, Kang-Sin; Park, Jeong-Hyuck
2015-10-23
We show that, without any extra physical degree introduced, the standard model can be readily reformulated as a double field theory. Consequently, the standard model can couple to an arbitrary stringy gravitational background in an O(4,4) T-duality covariant manner and manifest two independent local Lorentz symmetries, Spin(1,3)×Spin(3,1). While the diagonal gauge fixing of the twofold spin groups leads to the conventional formulation on the flat Minkowskian background, the enhanced symmetry makes the standard model more rigid, and also stringy, than it appeared. The CP violating θ term may no longer be allowed by the symmetry, and hence the strong CP problem can be solved. There are now stronger constraints imposed on the possible higher order corrections. We speculate that the quarks and the leptons may belong to the two different spin classes. PMID:26551099
Quantum spectral dimension in quantum field theory
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe
2016-03-01
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension dS of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension D. In particular, in the presence of higher momentum powers it changes with the scale, dropping from D in the infrared (IR) to a value dSUV ≤ D in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value dSUV = 2 for any dimension D.
Mean field theory of charged dendrimer molecules
NASA Astrophysics Data System (ADS)
Lewis, Thomas; Pryamitsyn, Victor; Ganesan, Venkat
2011-11-01
Using self-consistent field theory (SCFT), we study the conformational properties of polyelectrolyte dendrimers. We compare results for three different models of charge distributions on the polyelectrolytes: (1) a smeared, quenched charge distribution characteristic of strong polyelectrolytes; (2) a smeared, annealed charge distribution characteristic of weak polyelectrolytes; and (3) an implicit counterion model with Debye-Huckel interactions between the charged groups. Our results indicate that an explicit treatment of counterions is crucial for the accurate characterization of the conformations of polyelectrolyte dendrimers. In comparing the quenched and annealed models of charge distributions, annealed dendrimers were observed to modulate their charges in response to the density of polymer monomers, counterions, and salt ions. Such phenomena is not accommodated within the quenched model of dendrimers and is shown to lead to significant differences between the predictions of quenched and annealed model of dendrimers. In this regard, our results indicate that the average dissociated charge bar{α } inside the dendrimer serves as a useful parameter to map the effects of different parametric conditions and models onto each other. We also present comparisons to the scaling results proposed to explain the behavior of polyelectrolyte dendrimers. Inspired by the trends indicated by our results, we develop a strong segregation theory model whose predictions are shown to be in very good agreement with the numerical SCFT calculations.
Hamiltonian constraint in polymer parametrized field theory
Laddha, Alok; Varadarajan, Madhavan
2011-01-15
Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.
An Introduction to Boscovichian Unified Field Theory
NASA Astrophysics Data System (ADS)
Anderton, Roger James
2013-09-01
Boscovich proposed a unified theory in the 18th century, from this theory both quantum physics and Einstein's relativity was derived. Rather than look back at the history of how modern physics was developed, mainstream seems to go blindly onwards looking for a unified theory and ignoring this particular unified theory.
Parallel computing using a Lagrangian formulation
NASA Technical Reports Server (NTRS)
Liou, May-Fun; Loh, Ching Yuen
1991-01-01
A new Lagrangian formulation of the Euler equation is adopted for the calculation of 2-D supersonic steady flow. The Lagrangian formulation represents the inherent parallelism of the flow field better than the common Eulerian formulation and offers a competitive alternative on parallel computers. The implementation of the Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, a better than six times speed-up was achieved on a 8192-processor CM-2 over a single processor of a CRAY-2.
The IR-resummed Effective Field Theory of Large Scale Structures
Senatore, Leonardo; Zaldarriaga, Matias E-mail: matiasz@ias.edu
2015-02-01
We present a new method to resum the effect of large scale motions in the Effective Field Theory of Large Scale Structures. Because the linear power spectrum in ΛCDM is not scale free the effects of the large scale flows are enhanced. Although previous EFT calculations of the equal-time density power spectrum at one and two loops showed a remarkable agreement with numerical results, they also showed a 2% residual which appeared related to the BAO oscillations. We show that this was indeed the case, explain the physical origin and show how a Lagrangian based calculation removes this differences. We propose a simple method to upgrade existing Eulerian calculations to effectively make them Lagrangian and compare the new results with existing fits to numerical simulations. Our new two-loop results agrees with numerical results up to k∼ 0.6 h Mpc{sup −1} to within 1% with no oscillatory residuals. We also compute power spectra involving momentum which is significantly more affected by the large scale flows. We show how keeping track of these velocities significantly enhances the UV reach of the momentum power spectrum in addition to removing the BAO related residuals. We compute predictions for the real space correlation function around the BAO scale and investigate its sensitivity to the EFT parameters and the details of the resummation technique.
Topological field theory of dynamical systems.
Ovchinnikov, Igor V
2012-09-01
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the "edge of chaos." Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed. PMID:23020473
Topological field theory of dynamical systems
Ovchinnikov, Igor V.
2012-09-15
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the 'edge of chaos.' Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
Topological and differential geometrical gauge field theory
NASA Astrophysics Data System (ADS)
Saaty, Joseph
Recent Quantum Field Theory books have defined the topological charge (Q) in terms of the winding number (N). Contrary to this definition, my proof defines Q in terms of the quantum number (n). Defining Q in terms of n, instead of in terms of N, enables me to determine a precise value for Q. The solutions of all kinds of homotopy classification are referred to as instanton solutions, hence the terms homotopy classification and instanton solution will be used interchangeably. My proof replaces the use of these techniques with the use of the Dirac quantization condition, the covariant Dirac's equation, and the covariant Maxwell's equation. Unlike the earlier approaches, my proof accounts for the concept of the spin quantum number and the concept of time. Using the three methods noted above, my proof yields results not obtained by earlier methods. I have dealt similarly with the Pontryagin Index. I have used the Covariant Electrodynamics, in place of homotopy classification techniques, to create for the Pontryagin Index a proof that is alternative to the one cited in recent literature. The homotopy classification techniques gives an expression that excludes the fact that particles have spin quantum number. Therefore, the homotopy classification techniques does not really describe what the topological charge is in reality. I did derive an expression which does include the spin quantum numbers for particles and this has not been done before. Therefore, this will give a better idea for theoretical physicists about the nature of the topological charge. Contribution to knowledge includes creativity. I created an alternative method to the instanton solution for deriving an expression for the topological charge and this method led to new discoveries as a contribution to knowledge in which I found that topological charge for fermions cannot be quantized (to be quantized means to take discrete values only in integer steps), whereas the instanton solution cannot distinguish between bosons (quantized) and fermions (not quantized). Thus I produced results that were previously unobtainable. Furthermore, since topological charge takes place in Flat Spacetime, I investigated the quantization of the Curved Spacetime version of topological charge (Differential Geometrical Charge) by developing the differential geometrical Gauge Field Theory. It should be noted that the homotopy classification method is not at all applicable to Curved Spacetime. I also modified the Dirac equation in Curved Spacetime by using Einstein's field equation in order to account for the presence of matter. As a result, my method has allowed me to address four cases of topological charge (both spinless and spin one- half, in both Flat and in Curved Spacetime) whereas earlier methods had been blind to all but one of these cases (spinless in Flat Spacetime). (Abstract shortened by UMI.)
Hinterbichler, Kurt; Joyce, Austin; Khoury, Justin E-mail: joyceau@sas.upenn.edu
2012-06-01
The pseudo-conformal scenario is an alternative to inflation in which the early universe is described by an approximate conformal field theory on flat, Minkowski space. Some fields acquire a time-dependent expectation value, which breaks the flat space so(4,2) conformal algebra to its so(4,1) de Sitter subalgebra. As a result, weight-0 fields acquire a scale invariant spectrum of perturbations. The scenario is very general, and its essential features are determined by the symmetry breaking pattern, irrespective of the details of the underlying microphysics. In this paper, we apply the well-known coset technique to derive the most general effective lagrangian describing the Goldstone field and matter fields, consistent with the assumed symmetries. The resulting action captures the low energy dynamics of any pseudo-conformal realization, including the U(1)-invariant quartic model and the Galilean Genesis scenario. We also derive this lagrangian using an alternative method of curvature invariants, consisting of writing down geometric scalars in terms of the conformal mode. Using this general effective action, we compute the two-point function for the Goldstone and a fiducial weight-0 field, as well as some sample three-point functions involving these fields.
Obukhov, Yuri N.; Rubilar, Guillermo F.; Pereira, J. G.
2006-11-15
Conservation laws in gravitational theories with diffeomorphism and local Lorentz symmetry are studied. Main attention is paid to the construction of conserved currents and charges associated with an arbitrary vector field that generates a diffeomorphism on the spacetime. We further generalize previous results for the case of gravitational models described by quasi-invariant Lagrangians, that is, Lagrangians that change by a total derivative under the action of the local Lorentz group. The general formalism is then applied to the teleparallel models, for which the energy and the angular momentum of a Kerr black hole are calculated. The subsequent analysis of the results obtained demonstrates the importance of the choice of the frame.
NASA Astrophysics Data System (ADS)
Obukhov, Yuri N.; Rubilar, Guillermo F.; Pereira, J. G.
2006-11-01
Conservation laws in gravitational theories with diffeomorphism and local Lorentz symmetry are studied. Main attention is paid to the construction of conserved currents and charges associated with an arbitrary vector field that generates a diffeomorphism on the spacetime. We further generalize previous results for the case of gravitational models described by quasi-invariant Lagrangians, that is, Lagrangians that change by a total derivative under the action of the local Lorentz group. The general formalism is then applied to the teleparallel models, for which the energy and the angular momentum of a Kerr black hole are calculated. The subsequent analysis of the results obtained demonstrates the importance of the choice of the frame.
Effective Lagrangians and Current Algebra in Three Dimensions
NASA Astrophysics Data System (ADS)
Ferretti, Gabriele
In this thesis we study three dimensional field theories that arise as effective Lagrangians of quantum chromodynamics in Minkowski space with signature (2,1) (QCD3). In the first chapter, we explain the method of effective Langrangians and the relevance of current algebra techniques to field theory. We also provide the physical motivations for the study of QCD3 as a toy model for confinement and as a theory of quantum antiferromagnets (QAF). In chapter two, we derive the relevant effective Lagrangian by studying the low energy behavior of QCD3, paying particular attention to how the global symmetries are realized at the quantum level. In chapter three, we show how baryons arise as topological solitons of the effective Lagrangian and also show that their statistics depends on the number of colors as predicted by the quark model. We calculate mass splitting and magnetic moments of the soliton and find logarithmic corrections to the naive quark model predictions. In chapter four, we drive the current algebra of the theory. We find that the current algebra is a co -homologically non-trivial generalization of Kac-Moody algebras to three dimensions. This fact may provide a new, non -perturbative way to quantize the theory. In chapter five, we discuss the renormalizability of the model in the large-N expansion. We prove the validity of the non-renormalization theorem and compute the critical exponents in a specific limiting case, the CP^ {N-1} model with a Chern-Simons term. Finally, chapter six contains some brief concluding remarks.
The field theory of specific heat
NASA Astrophysics Data System (ADS)
Gusev, Yu. V.
2016-01-01
Finite temperature quantum field theory in the heat kernel method is used to study the heat capacity of condensed matter. The lattice heat is treated à la P. Debye as energy of the elastic (sound) waves. The dimensionless functional of free energy is re-derived with a cut-off parameter and used to obtain the specific heat of crystal lattices. The new dimensionless thermodynamical variable is formed as Planck's inverse temperature divided by the lattice constant. The dimensionless constant, universal for the class of crystal lattices, which determines the low temperature region of molar specific heat, is introduced and tested with the data for diamond lattice crystals. The low temperature asymptotics of specific heat is found to be the fourth power in temperature instead of the cubic power law of the Debye theory. Experimental data for the carbon group elements (silicon, germanium) and other materials decisively confirm the quartic law. The true low temperature regime of specific heat is defined by the surface heat, therefore, it depends on the geometrical characteristics of the body, while the absolute zero temperature limit is geometrically forbidden. The limit on the growth of specific heat at temperatures close to critical points, known as the Dulong-Petit law, appears from the lattice constant cut-off. Its value depends on the lattice type and it is the same for materials with the same crystal lattice. The Dulong-Petit values of compounds are equal to those of elements with the same crystal lattice type, if one mole of solid state matter were taken as the Avogadro number of the composing atoms. Thus, the Neumann-Kopp law is valid only in some special cases.
The Physical Renormalization of Quantum Field Theories
Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC
2007-02-20
The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi-scale analytic renormalization scheme based on gauge-invariant Green's functions, in which the scale ambiguity problem is reduced since physical kinematic invariants determine the arguments of the couplings.
Mean Field Theories of Icosahedral Quasicrystals.
NASA Astrophysics Data System (ADS)
Troian, Sandra Marina
In 1984 Shechtman et al. discovered a metallic solid (Al(,86)Mn(,14)) with diffraction spots as sharp as those of crystals but with icosahedral point group symmetry, known to be incompatible with translational symmetry. One of the interesting crystallographic questions posed by the discovery of quasicrystals, as these materials are now called, is why does the atomic density assume an icosahedrally symmetric configuration in preference to conventional periodic crystalline forms. To address this question, we use a phenomenological approach based on the Landau theory of crystal formation (Landau, 1937) to ascertain whether any of the conventional elementary approaches to crystal formation might not contain metastable (or even stable) quasicrystalline solutions hitherto overlooked because of the almost universal prejudice that positional ordering must be periodic. Alexander and McTague (1978) touched on the possibility of icosahedrally symmetric structures using a (single order parameter) Landau free energy. We reexamine and extend their model and find that there are three distinct icosahedral stationary points to the free energy, although none of them is ever globally stable compared with more conventional competing structures like the body-centered cubic, hexagonal, or smectic. Which periodic form is favored depends on the temperature range investigated. We find that two of these stationary points are not even local minima of the free energy. We generalize this model by constructing a Landau theory for two or three-component systems, which appear to give a region of the phase diagram in which icosahedral quasicrystalline ordering is the state of lowest free energy. The quasicrystals are stabilized by special geometric ratios between the length scales characterizing the components. Three components are required to stabilize a two-dimensional quasicrystal but two components suffice to stabilize a three-dimensional one. We present results for two different ratios studied. We also rederive and generalize a model free energy presented by Kalugin et al. to show that their original conclusion of a metastable quasicrystal is invalidated by the inclusion of a local quartic term in the free energy. Lastly, we review three other mean field theories recently proposed to explain the existence of quasicrystals.
Generalization of the Skyrme model for the unified theory of pions and nucleons
Kindo, T.; Yukawa, T.
1988-09-01
Skyrme's Lagrangian is generalized within the pion field alone to include all possible terms which appear in the chiral perturbation theory up to fourth order in the field derivative and the symmetry-breaking mass. The parameters entering in the Lagrangian are fixed from the low-energy pion properties. Adding a sixth-order term to the Lagrangian for stabilization the hedgehog soliton is quantized semiclassically. Static properties of the soliton reproduce those of the nucleon with fairly good accuracy.
Generalized BRST symmetry for arbitrary spin conformal field theory
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker; Mandal, Bhabani Prasad
2015-05-01
We develop the finite field-dependent BRST (FFBRST) transformation for arbitrary spin-s conformal field theories. We discuss the novel features of the FFBRST transformation in these systems. To illustrate the results we consider the spin-1 and spin-2 conformal field theories in two examples. Within the formalism we found that FFBRST transformation connects the generating functionals of spin-1 and spin-2 conformal field theories in linear and non-linear gauges. Further, the conformal field theories in the framework of FFBRST transformation are also analyzed in Batalin-Vilkovisky (BV) formulation to establish the results.
Gravitational consequences of modern field theories
NASA Technical Reports Server (NTRS)
Horowitz, Gary T.
1989-01-01
Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.
Could reggeon field theory be an effective theory for QCD in the Regge limit?
NASA Astrophysics Data System (ADS)
Bartels, Jochen; Contreras, Carlos; Vacca, G. P.
2016-03-01
In this paper we investigate the possibility whether, in the extreme limit of high energies and large transverse distances, reggeon field theory might serve as an effective theory of high energy scattering for strong interactions. We analyse the functional renormalization group equations (flow equations) of reggeon field theory and search for fixed points in the space of (local) reggeon field theories. We study in complementary ways the candidate for the scaling solution, investigate its main properties and briefly discuss possible physical interpretations.
On the minimality of the order p6 chiral Lagrangian
NASA Astrophysics Data System (ADS)
Ruiz-Femenía, Pedro; Zahiri-Abyaneh, Mehran
2015-12-01
A method to find relations between the operators in the mesonic Lagrangian of Chiral Perturbation Theory at order p6 is presented. The procedure can be used to establish if the basis of operators in the Lagrangian is minimal. As an example, we apply the method to the two-flavor case in the absence of scalar and pseudo-scalar sources (s = p = 0), and conclude that the minimal Lagrangian contains 27 independent operators.
Gravitational Descendants in Symplectic Field Theory
NASA Astrophysics Data System (ADS)
Fabert, Oliver
2011-02-01
It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown using the ideas in Okounkov and Pandharipande (Ann Math 163(2):517-560, 2006) that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits, the gravitational descendants have a geometric interpretation in terms of branching conditions, we follow the ideas in Cieliebak and Latschev (
Effective field theory analysis of Higgs naturalness
NASA Astrophysics Data System (ADS)
Bar-Shalom, Shaouly; Soni, Amarjit; Wudka, Jose
2015-07-01
Assuming the presence of physics beyond the Standard Model (SM) with a characteristic scale M ˜O (10 ) TeV , we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the complete set of higher-dimensional effective operators (at any dimension n ≥5 ) that give the leading one-loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff and discuss the (fine-) tuning between these terms and the SM one-loop contribution, which is required in order to alleviate the little hierarchy problem. We then show that this tuning can be translated into a condition for naturalness in the underlying new physics, a condition we denote by "EFT naturalness" and which we express as constraints on the corresponding higher-dimensional operator coefficients up to the scale of the effective action Λ
Quarkonium hybrids with nonrelativistic effective field theories
NASA Astrophysics Data System (ADS)
Berwein, Matthias; Brambilla, Nora; Tarrús Castellà, Jaume; Vairo, Antonio
2015-12-01
We construct a nonrelativistic effective field theory description of heavy quarkonium hybrids from QCD. We identify the symmetries of the system made of a heavy quark, a heavy antiquark, and glue in the static limit. Corrections to this limit can be obtained order by order in an expansion in the inverse of the mass m of the heavy quark. At order 1 /m in the expansion, we obtain, at the level of potential nonrelativistic QCD, a system of coupled Schrödinger equations that describes hybrid spin-symmetry multiplets, including the mixing of different static energies into the hybrid states, an effect known as Λ doubling in molecular physics. In the short distance, the static potentials depend on two nonperturbative parameters, the gluelump mass and the quadratic slope, which can be determined from lattice calculations. We adopt a renormalon subtraction scheme for the calculation of the perturbative part of the potential. We numerically solve the coupled Schrödinger equations and obtain the masses for the lowest lying spin-symmetry multiplets for c c ¯, b c ¯, and b b ¯ hybrids. The Λ -doubling effect breaks the degeneracy between opposite-parity spin-symmetry multiplets and lowers the mass of the multiplets that get mixed contributions of different static energies. We compare our findings to the experimental data, direct lattice computations, and sum rule calculations, and discuss the relation to the Born-Oppenheimer approximation.
Quantifying truncation errors in effective field theory
NASA Astrophysics Data System (ADS)
Furnstahl, R. J.; Klco, N.; Phillips, D. R.; Wesolowski, S.
2015-10-01
Bayesian procedures designed to quantify truncation errors in perturbative calculations of QCD observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. Computation of these intervals requires specification of prior probability distributions (``priors'') for the expansion coefficients. By encoding expectations about the naturalness of these coefficients, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. It also permits exploration of the ways in which such error bars are, and are not, sensitive to assumptions about EFT-coefficient naturalness. We demonstrate the calculation of Bayesian DOB intervals for the EFT truncation error in some representative cases and explore several methods by which the convergence properties of the EFT for a set of observables may be used to check the statistical consistency of the EFT expansion parameter. Supported in part by the NSF and the DOE.
Quantifying truncation errors in effective field theory
NASA Astrophysics Data System (ADS)
Furnstahl, R. J.; Klco, N.; Phillips, D. R.; Wesolowski, S.
2015-08-01
Bayesian procedures designed to quantify truncation errors in perturbative calculations of quantum chromodynamics observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. Computation of these intervals requires specification of prior probability distributions ("priors") for the expansion coefficients. By encoding expectations about the naturalness of these coefficients, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. It also permits exploration of the ways in which such error bars are, and are not, sensitive to assumptions about EFT-coefficient naturalness. We first demonstrate the calculation of Bayesian probability distributions for the EFT truncation error in some representative examples and then focus on the application of chiral EFT to neutron-proton scattering. Epelbaum, Krebs, and Meißner recently articulated explicit rules for estimating truncation errors in such EFT calculations of few-nucleon-system properties. We find that their basic procedure emerges generically from one class of naturalness priors considered and that all such priors result in consistent quantitative predictions for 68% DOB intervals. We then explore several methods by which the convergence properties of the EFT for a set of observables may be used to check the statistical consistency of the EFT expansion parameter.
Protected gates for topological quantum field theories
NASA Astrophysics Data System (ADS)
Beverland, Michael E.; Buerschaper, Oliver; Koenig, Robert; Pastawski, Fernando; Preskill, John; Sijher, Sumit
2016-02-01
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
Global Lagrangian Atmospheric Dispersion Model
NASA Astrophysics Data System (ADS)
Lukyanov, A. N.; Gan'shin, A. V.; Zhuravlev, R. V.; Maksyutov, Sh. Sh.; Varlagin, A. V.
2015-09-01
The Global Lagrangian Atmospheric Dispersion Model (GLADIM) is described. GLADIM is based on the global trajectory model, which had been developed earlier and uses fields of weather parameters from different atmospheric reanalysis centers for calculations of trajectories of air mass that include trace gases. GLADIM includes the parameterization of turbulent diffusion and allows the forward calculation of concentrations of atmospheric tracers at nodes of a global regular grid when a source is specified. Thus, GLADIM can be used for the forward simulation of pollutant propagation (volcanic ash, radionuclides, and so on). Working in the reverse direction, GLADIM allows the detection of remote sources that mainly contribute to the tracer concentration at an observation point. This property of Lagrangian models is widely used for data analysis and the reverse modeling of emission sources of a pollutant specified. In this work we describe the model and some results of its validation through a comparison with results of a similar model and observation data.
Effective Lagrangian for Nonrelativistic Systems
NASA Astrophysics Data System (ADS)
Watanabe, Haruki; Murayama, Hitoshi
2014-07-01
The effective Lagrangian for Nambu-Goldstone bosons (NGBs) in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing 1 dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in 1+1 dimensions.
Next-to-simplest quantum field theories
Lal, Shailesh; Raju, Suvrat
2010-05-15
We describe new on-shell recursion relations for tree amplitudes in N=1 and N=2 gauge theories and use these to show that the structure of the one-loop S-matrix in pure (i.e. without any matter) N=1 and N=2 gauge theories resembles that of pure Yang-Mills theory. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth- and sixth-order indices of the matter representation, respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and nonsupersymmetric theories that are free of bubbles. These theories see simplifications in their S-matrices that cannot be deduced just from naive power-counting. In particular, our results indicate that one-loop scattering amplitudes in the N=2, SU(N) theory with a symmetric tensor hypermultiplet and an antisymmetric tensor hypermultiplet are simple like those in the N=4 theory.
The Field Line Resonance: Observation and Theory
NASA Astrophysics Data System (ADS)
Fenrich, Frances Rose Erna
This thesis is an observational and theoretical study of field line resonances (FLRs) found to occur on magnetic shells in the Earth's magnetosphere. These resonances are actually standing shear Alfven waves in the ultra-low frequency (ULF) regime, generated through mode coupling to fast compressional magnetohydrodynamic waves in the outer magnetosphere. FLRs may be signatures of fundamental processes by which energy is transported from the solar wind to the ionosphere and it is therefore important to study their characteristics and fully understand their generation mechanisms. Numerous FLR events have been identified and analyzed using the Super Dual Auroral Radar Network (SuperDARN). This network is a system of high-frequency (HF) radars which provides a global-scale view of the plasma convection in the F-region of the high-latitude ionosphere. The oscillations in plasma flow associated with an FLR are superimposed upon the background convective flow and can be used to determine many characteristics of the FLR such as frequency, phase, location, and propagation velocities. A compilation of the observations has yielded some very interesting results. The most notable of these is that the FLRs repeatedly occur at the same discrete and stable frequencies, i.e., 1.3, 1.9, and 2.5 mHz, independent of local time and azimuthal wave number, m. They are also classifiable into two distinct types: those with small azimuthal wave number (m<17), and those with large azimuthal wave number (m>17). The fact that the two different wave types have numerous similarities is very important since it suggests that the same driving mechanism is responsible for the initiation of both types of resonance. The apparent growth rates of the FLRs show a striking correlation with the azimuthal wave number of the resonance. The observed high-m resonances have amplitudes that increase with time, indicating positive growth rates, while the low-m resonances have decreasing amplitudes, indicating negative growth rates. The resonance growth rates and latitudinal phase shifts, a decrease for low-m modes and an increase for high-m modes, are found to be determined by the direction of the Poynting flux in the system. In the case of the high-m resonance, an internal driver is present which is able to couple to the system and give Poynting flux out of the resonance region. The internal driver is most likely in the form of a wave-particle interaction. The final portion of this thesis concerns the development of a theoretical model for the FLR driving mechanism. The most commonly accepted theory, the magnetospheric waveguide/cavity mode model, postulates that the magnetosphere acts as a waveguide or cavity which can generate a set of monochromatic fast wave eigenmodes which then couple to the FLRs. A review of this theory has shown that it falls short of explaining many of the experimental observations. Thus alternate theories capable of explaining the observations are explored. A new model, the magnetosheath waveguide model, is examined in detail and is shown to be very successful in its ability to explain the existence of the discrete FLRs.
Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory
NASA Astrophysics Data System (ADS)
Manuel, Cristina; Torres-Rincon, Juan M.
2014-10-01
We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian. The Berry connection naturally emerges in the diagonalization process to modify the classical equations of motion of a fermion in an electromagnetic field. We also see that the fermion and antifermion dispersion relations are corrected at first order in the Planck constant by the Berry curvature, as previously derived by Son and Yamamoto for the particular case of vanishing temperature. Our approach does not require knowledge of the state of the system, and thus it can also be applied at high temperature. We provide support for our result by an alternative computation using an effective field theory for fermions and antifermions: the on-shell effective field theory. In this formalism, the off-shell fermionic modes are integrated out to generate an effective Lagrangian for the quasi-on-shell fermions/antifermions. The dispersion relation at leading order exactly matches the result from the semiclassical diagonalization. From the transport equation, we explicitly show how the axial and gauge anomalies are not modified at finite temperature and density despite the incorporation of the new dispersion relation into the distribution function.
Field theory on R× S 3 topology. VI: Gravitation
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malin, S.
1987-04-01
We extend to curved space-time the field theory on R×S3 topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU2 gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.
Gauge field theory for the Poincare-Weyl group
Babourova, O. V.; Frolov, B. N.; Zhukovsky, V. Ch.
2006-09-15
On the basis of the general principles of a gauge field theory, the gauge theory for the Poincare-Weyl group is constructed. It is shown that tetrads are not true gauge fields, but represent functions of true gauge fields: Lorentzian, translational, and dilatational ones. The equations for gauge fields are obtained. Geometrical interpretation of the theory is developed demonstrating that as a result of localization of the Poincare-Weyl group the space-time becomes a Weyl-Cartan space. The geometrical interpretation of a dilaton field as a component of the metric tensor of a tangent space in Weyl-Cartan geometry is also proposed.
Extended gyrokinetic field theory for time-dependent magnetic confinement fields
Sugama, H.; Watanabe, T.-H.; Nunami, M.
2014-01-15
A gyrokinetic system of equations for turbulent toroidal plasmas in time-dependent axisymmetric background magnetic fields is derived from the variational principle. Besides governing equations for gyrocenter distribution functions and turbulent electromagnetic fields, the conditions which self-consistently determine the background magnetic fields varying on a transport time scale are obtained by using the Lagrangian, which includes the constraint on the background fields. Conservation laws for energy and toroidal angular momentum of the whole system in the time-dependent background magnetic fields are naturally derived by applying Noether's theorem. It is shown that the ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work agree with the results from the conventional recursive formulation with the WKB representation except that collisional effects are disregarded here.
Reggeon Field Theory and the phases of QCD
White, A.R.
1987-07-21
We propose a Reggeon Field Theory phase diagram involving Sub-critical and Super-critical Pomeron behavior and the Expanding Disc. We describe the derivation of Reggeon Field Theory from QCD using infra-red analysis of the reggeon diagrams of the spontaneously broken theory. Matching the Reggeon Field Theory phase-diagram to that of lattice QCD with many fermions has significant implications for the chiral properties of continuum QCD when the number of flavors is less than the maximum allowed by asymptotic freedom. 19 refs., 7 figs.
Entanglement entropy in Galilean conformal field theories and flat holography.
Bagchi, Arjun; Basu, Rudranil; Grumiller, Daniel; Riegler, Max
2015-03-20
We present the analytical calculation of entanglement entropy for a class of two-dimensional field theories governed by the symmetries of the Galilean conformal algebra, thus providing a rare example of such an exact computation. These field theories are the putative holographic duals to theories of gravity in three-dimensional asymptotically flat spacetimes. We provide a check of our field theory answers by an analysis of geodesics. We also exploit the Chern-Simons formulation of three-dimensional gravity and adapt recent proposals of calculating entanglement entropy by Wilson lines in this context to find an independent confirmation of our results from holography. PMID:25839258
Effective field theory of broken spatial diffeomorphisms
NASA Astrophysics Data System (ADS)
Lin, Chunshan; Labun, Lance Z.
2016-03-01
We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constant for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. We discuss several examples relevant to theories of massive gravity.
Mapping of the density functional theory on the crystal field theory of rare earth systems
NASA Astrophysics Data System (ADS)
Fänle, M.; Fähnle, M.
1995-11-01
By mapping the density functional theory on the crystal field theory within a first order perturbation approach it is proven that the exchange-correlation potential has to be included into the definition of the crystal field parameters, as suggested by Novák and coworkers. The validity of the first order theory yielding crystal field parameters which are independent of the state of the 4f shell is discussed.
GravitoMagnetic Field in Tensor-Vector-Scalar Theory
Exirifard, Qasem
2013-04-01
We study the gravitomagnetism in the TeVeS theory. We compute the gravitomagnetic field that a slow moving mass distribution produces in its Newtonian regime. We report that the consistency between the TeVeS gravitomagnetic field and that predicted by the Einstein-Hilbert theory leads to a relation between the vector and scalar coupling constants of the theory. We translate the Lunar Laser Ranging measurement's data into a constraint on the deviation from this relation.
Quantum field theory of forward rates with stochastic volatility.
Baaquie, Belal E
2002-05-01
In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are analyzed, first when volatility is taken to be a function of the forward rates, and second when volatility is taken to be an independent quantum field. Since volatility is a positive valued quantum field, the full theory turns out to be an interacting nonlinear quantum field theory in two dimensions. The state space and Hamiltonian for the interacting theory are obtained, and shown to have a nontrivial structure due to the manifold moving with a constant velocity. The no arbitrage condition is reformulated in terms of the Hamiltonian of the system, and then exactly solved for the nonlinear interacting case. PMID:12059662
Effective field theory: A modern approach to anomalous couplings
Degrande, Céline; Centre for Particle Physics and Phenomenology , Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve ; Greiner, Nicolas; Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München ; Kilian, Wolfgang; University of Siegen, Fachbereich Physik, D-57068 Siegen ; Mattelaer, Olivier; Mebane, Harrison; Stelzer, Tim; Willenbrock, Scott; Zhang, Cen; Centre for Particle Physics and Phenomenology , Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve
2013-08-15
We advocate an effective field theory approach to anomalous couplings. The effective field theory approach is the natural way to extend the standard model such that the gauge symmetries are respected. It is general enough to capture any physics beyond the standard model, yet also provides guidance as to the most likely place to see the effects of new physics. The effective field theory approach also clarifies that one need not be concerned with the violation of unitarity in scattering processes at high energy. We apply these ideas to pair production of electroweak vector bosons. -- Highlights: •We discuss the advantages of effective field theories compared to anomalous couplings. •We show that one need not be concerned with unitarity violation at high energy. •We discuss the application of effective field theory to weak boson physics.
Infinities in Quantum Field Theory and in Classical Computing: Renormalization Program
NASA Astrophysics Data System (ADS)
Manin, Yuri I.
Introduction. The main observable quantities in Quantum Field Theory, correlation functions, are expressed by the celebrated Feynman path integrals. A mathematical definition of them involving a measure and actual integration is still lacking. Instead, it is replaced by a series of ad hoc but highly efficient and suggestive heuristic formulas such as perturbation formalism. The latter interprets such an integral as a formal series of finite-dimensional but divergent integrals, indexed by Feynman graphs, the list of which is determined by the Lagrangian of the theory. Renormalization is a prescription that allows one to systematically "subtract infinities" from these divergent terms producing an asymptotic series for quantum correlation functions. On the other hand, graphs treated as "flowcharts", also form a combinatorial skeleton of the abstract computation theory. Partial recursive functions that according to Church's thesis exhaust the universe of (semi)computable maps are generally not everywhere defined due to potentially infinite searches and loops. In this paper I argue that such infinities can be addressed in the same way as Feynman divergences. More details can be found in [9,10].
Nonequilibrium Chiral Dynamics and Effective Lagrangians
NASA Astrophysics Data System (ADS)
Nicola, A. Gómez
2002-04-01
We review our recent work on Chiral Lagrangians out of thermal equilibrium, which are introduced to analyse the pion gas formed after a Relativistic Heavy Ion Collision. Chiral Perturbation Theory is extended by letting fπ be time dependent and allows to describe explosive production of pions in parametric resonance. This mechanism could be relevant if hadronization occurs at the chiral phase transition.
On the application of the field-redefinition theorem to the heterotic superstring theory
NASA Astrophysics Data System (ADS)
Pollock, M. D.
2015-05-01
The ten-dimensional effective action which defines the heterotic superstring theory at low energy is constructed by hypothesis in such a way that the resulting classical equation of motion for the space-time metric simultaneously implies the vanishing of the beta-function for the N = 1 supersymmetric non-linear sigma-model on the world sheet. At four-loop order it was found by Grisaru and Zanon (see also Freeman et al.) that the effective Lagrangian so constructed differs in the numerical coefficient of the term from that obtained directly from the four-point gravitational scattering amplitude. The two expressions can be related via a metric field redefinition , activation of which, however, results in the appearance of ghosts at higher gravitational order , n > 4, as shown by Lawrence. Here, we prove, after reduction of to the physical dimensionality D = 4, that the corresponding field redefinition yields the identity g' ij = g ij , signified by L 3/ R = 0, in a Friedmann space-time generated by a perfect-fluid source characterized by adiabatic index γ ≡ 1 + p/ ρ, where p is the pressure and ρ is the energy density, if, and only if, κ 6 ρ 3 γ 2( γ - 1) = 0. That is, the theory remains free of ghosts in Minkowski space ρ = 0, in a maximally symmetric space-time γ = 0, or in a dust Universe γ = 1. Further aspects of ghost freedom and dimensional reduction, especially to D = 4, are discussed.
Heavy Quarks, QCD, and Effective Field Theory
Thomas Mehen
2012-10-09
The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E#11;ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e#11;ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi#12;eld theoretic de#12;nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.
Lagrangian perturbations and the matter bispectrum I: fourth-order model for non-linear clustering
Rampf, Cornelius; Buchert, Thomas E-mail: buchert@obs.univ-lyon1.fr
2012-06-01
We investigate the Lagrangian perturbation theory of a homogeneous and isotropic universe in the non-relativistic limit, and derive the solutions up to the fourth order. These solutions are needed for example for the next-to-leading order correction of the (resummed) Lagrangian matter bispectrum, which we study in an accompanying paper. We focus on flat cosmologies with a vanishing cosmological constant, and provide an in-depth description of two complementary approaches used in the current literature. Both approaches are solved with two different sets of initial conditions both appropriate for modelling the large-scale structure. Afterwards we consider only the fastest growing mode solution, which is not affected by either of these choices of initial conditions. Under the reasonable approximation that the linear density contrast is evaluated at the initial Lagrangian position of the fluid particle, we obtain the nth-order displacement field in the so-called initial position limit: the nth order displacement field consists of 3(n-1) integrals over n linear density contrasts, and obeys self-similarity. Then, we find exact relations between the series in Lagrangian and Eulerian perturbation theory, leading to identical predictions for the density contrast and the peculiar-velocity divergence up to the fourth order.
Splitting fields and general differential Galois theory
Trushin, Dmitry V
2010-11-11
An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions. Bibliography: 14 titles.
NASA Astrophysics Data System (ADS)
Singh, BirBikram; Bhuyan, M.; Patra, S. K.; Gupta, Raj K.
2012-02-01
A microscopic nucleon-nucleon (NN) interaction is derived from the popular relativistic-mean-field (RMF) theory Lagrangian and used to obtain the optical potential by folding it with the RMF densities of cluster and daughter nuclei. The NN-interaction is remarkably related to the inbuilt fundamental parameters of RMF theory, and the results of the application of the so obtained optical potential, made to exotic cluster radioactive decays and α+α scattering, are found comparable to that for the well-known, phenomenological M3Y effective NN-interaction. The RMF-based NN-interaction can also be used to calculate a number of other nuclear observables.
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1992-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. Unlike the Lagrangian method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.
Lorentz symmetry breaking as a quantum field theory regulator
Visser, Matt
2009-07-15
Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just 'how much' Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [Phys. Rev. D 79, 084008 (2009)] on 3+1 dimensional quantum gravity.
On the stability of the asymptotically free scalar field theories
Shalaby, A M.
2015-03-30
Asymptotic freedom plays a vital role in our understanding of the theory of particle interactions. To have this property, one has to resort to a Non-abelian gauge theory with the number of colors equal to or greater than three (QCD). However, recent studies have shown that simple scalar field theories can possess this interesting property. These theories have non-Hermitian effective field forms but their classical potentials are bounded from above. In this work, we shall address the stability of the vacua of the bounded from above (−Φ{sup 4+n}) scalar field theories. Moreover, we shall cover the effect of the distribution of the Stokes wedges in the complex Φ-plane on the features of the vacuum condensate within these theories.
Open superstring field theory on the restricted Hilbert space
NASA Astrophysics Data System (ADS)
Konopka, Sebastian; Sachs, Ivo
2016-04-01
It appears that the formulation of an action for the Ramond sector of open superstring field theory requires to either restrict the Hilbert space for the Ramond sector or to introduce auxiliary fields with picture -3/2. The purpose of this note is to clarify the relation of the restricted Hilbert space with other approaches and to formulate open superstring field theory entirely in the small Hilbert space.
Mean-field theory for Bose-Hubbard model under a magnetic field
Oktel, M. Oe.; Tanatar, B.; Nita, M.
2007-01-15
We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.
Soft theorems from conformal field theory
NASA Astrophysics Data System (ADS)
Lipstein, Arthur E.
2015-06-01
Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambtwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.
Bits and Pieces in Logarithmic Conformal Field Theory
NASA Astrophysics Data System (ADS)
Flohr, Michael A. I.
These are notes of my lectures held at the first School & Workshop on Logarithmic Conformal Field Theory and its Applications, September 2001 in Tehran, Iran. These notes cover only selected parts of the by now quite extensive knowledge on logarithmic conformal field theories. In particular, I discuss the proper generalization of null vectors towards the logarithmic case, and how these can be used to compute correlation functions. My other main topic is modular invariance, where I discuss the problem of the generalization of characters in the case of indecomposable representations, a proposal for a Verlinde formula for fusion rules and identities relating the partition functions of logarithmic conformal field theories to such of well known ordinary conformal field theories. The two main topics are complemented by some remarks on ghost systems, the Haldane-Rezayi fractional quantum Hall state, and the relation of these two to the logarithmic c=-2 theory.
Extended theories of gravitation
NASA Astrophysics Data System (ADS)
Fatibene, Lorenzo; Garruto, Simon
2016-04-01
In this paper, we shall review the equivalence between Palatini-f(ℛ) theories and Brans-Dicke (BD) theories at the level of action principles. We shall define the Helmholtz Lagrangian associated to Palatini-f(ℛ) theory and we will define some transformations which will be useful to recover Einstein frame and BD frame. We shall see an explicit example of matter field and we will discuss how the conformal factor affects the physical quantities.
Perturbative Aspects of Low-Dimensional Quantum Field Theory
Wardaya, Asep Y.; Zen, Freddy P.; Kosasih, Jusak S.; , Triyanta; Hartanto, Andreas
2010-06-22
We investigate the low-dimensional applications of Quantum Field Theory (QFT), namely Chern-Simons-Witten Theory (CSWT) and Affine Toda Field Theory (ATFT) in 3- and 2- dimensions. We discuss the perturbative aspects of both theories and compare the results to the exact solutions obtained nonperturbatively. For the three dimensions CSWT case, the perturbative term agree with the nonperturbative polynomial invariants up to third order of the coupling constant 1/k. In the two dimensions ATFT, we investigate the perturbative aspect of S-matrices for A{sub 1}{sup (1)} case in eighth order of the coupling constant {beta}.
NASA Technical Reports Server (NTRS)
Lee, C. H.
1978-01-01
A 3-D finite element program capable of simulating the dynamic behavior in the vicinity of the impact point, together with predicting the dynamic response in the remaining part of the structural component subjected to high velocity impact is discussed. The finite algorithm is formulated in a general moving coordinate system. In the vicinity of the impact point contained by a moving failure front, the relative velocity of the coordinate system will approach the material particle velocity. The dynamic behavior inside the region is described by Eulerian formulation based on a hydroelasto-viscoplastic model. The failure front which can be regarded as the boundary of the impact zone is described by a transition layer. The layer changes the representation from the Eulerian mode to the Lagrangian mode outside the failure front by varying the relative velocity of the coordinate system to zero. The dynamic response in the remaining part of the structure described by the Lagrangian formulation is treated using advanced structural analysis. An interfacing algorithm for coupling CELFE with NASTRAN is constructed to provide computational capabilities for large structures.
Frame-like Lagrangians and presymplectic AKSZ-type sigma models
NASA Astrophysics Data System (ADS)
Alkalaev, Konstantin; Grigoriev, Maxim
2014-07-01
We study supergeometric structures underlying frame-like Lagrangians. We show that for the theory in n space-time dimensions both the frame-like Lagrangian and its gauge symmetries are encoded in the target supermanifold equipped with the odd vector field, the closed two-form of ghost degree n-1, and the scalar potential of ghost degree n. These structures satisfy a set of compatibility conditions ensuring the gauge invariance of the theory. The Lagrangian and the gauge symmetries have the same structures as those of AKSZ sigma model so that frame-like formulation can be seen as its presymplectic generalization. In contrast to the conventional AKSZ model, the generalization allows to describe systems with local degrees of freedom in terms of finite-dimensional target space. We argue that the proposed frame-like approach is directly related de Donder-Weyl polymomentum Hamiltonian formalism. Along with the standard field-theoretical examples like Einstein-Yang-Mills theory, we consider free higher spin fields, multi-frame gravity and parametrized systems. In particular, we propose the frame-like action for free totally symmetric massless fields that involves all higher spin connections on an equal footing.
Semiclassical theory of unimolecular dissociation induced by a laser field
NASA Technical Reports Server (NTRS)
Yuan, J.-M.; George, T. F.
1978-01-01
A semiclassical nonperturbative theory of direct photodissociation in a laser field is developed in which photon absorption and dissociation are treated in a unified fashion. This is achieved by visualizing nuclear dynamics as a representative particle moving on electronic-field surfaces. Methods are described for calculating dissociation rates and probabilities by Monte Carlo selection of initial conditions and integration of classical trajectories on these surfaces. This unified theory reduces to the golden rule expression in the weak-field and short-time limits, and predicts nonlinear behavior, i.e., breakdown of the golden rule expression in intense fields. Field strengths above which lowest-order perturbation theory fails to work have been estimated for some systems. Useful physical insights provided by the electronic-field representation have been illustrated. Intense field effects are discussed which are amenable to experimental observation. The semiclassical methods used here are also applicable to multiple-surface dynamics in fieldfree unimolecular and bimolecular reactions.
One-loop effective lagrangians after matching
NASA Astrophysics Data System (ADS)
del Aguila, F.; Kunszt, Z.; Santiago, J.
2016-05-01
We discuss the limitations of the covariant derivative expansion prescription advocated to compute the one-loop Standard Model (SM) effective lagrangian when the heavy fields couple linearly to the SM. In particular, one-loop contributions resulting from the exchange of both heavy and light fields must be explicitly taken into account through matching because the proposed functional approach alone does not account for them. We review a simple case with a heavy scalar singlet of charge -1 to illustrate the argument. As two other examples where this matching is needed and this functional method gives a vanishing result, up to renormalization of the heavy sector parameters, we re-evaluate the one-loop corrections to the T-parameter due to a heavy scalar triplet with vanishing hypercharge coupling to the Brout-Englert-Higgs boson and to a heavy vector-like quark singlet of charged 2 / 3 mixing with the top quark, respectively. In all cases we make use of a new code for matching fundamental and effective theories in models with arbitrary heavy field additions.
Incorporation of generalized uncertainty principle into Lifshitz field theories
Faizal, Mir; Majumder, Barun
2015-06-15
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Effective field theories of baryons and mesons, or, what do quarks do?
Keaton, G.L.
1995-06-26
This thesis is an attempt to understand the properties of the protons, pions and other hadrons in terms of their fundamental building blocks. In the first chapter the author reviews several of the approaches that have already been developed. The Nambu-Jona-Lasinio model offers the classic example of a derivation of meson properties from a quark Lagrangian. The chiral quark model encodes much of the intuition acquired in recent decades. The author also discusses the non-linear sigma model, the Skyrme model, and the constituent quark model, which is one of the oldest and most successful models. In the constituent quark model, the constituent quark appears to be different from the current quark that appears in the fundamental QCD Lagrangian. Recently it was proposed that the constituent quark is a topological soliton. In chapter 2 the author investigates this soliton, calculating its mass, radius, magnetic moment, color magnetic moment, and spin structure function. Within the approximations used, the magnetic moments and spin structure function cannot simultaneously be made to agree with the constituent quark model. In chapter 3 the author uses a different plan of attack. Rather than trying to model the constituents of the baryon, he begins with an effective field theory of baryons and mesons, with couplings and masses that are simply determined phenomenologically. Meson loop corrections to baryon axial currents are then computed in the 1/N expansion. It is already known that the one-loop corrections are suppressed by a factor 1/N; here it is shown that the two-loop corrections are suppressed by 1/N{sup 2}. To leading order, these corrections are exactly the same as would be calculated in the constituent quark model. This method therefore offers a different approach to the constituent quark.
A New Lorentz Violating Nonlocal Field Theory From String-Theory
Ganor, Ori J.
2007-10-04
A four-dimensional field theory with a qualitatively new type of nonlocality is constructed from a setting where Kaluza-Klein particles probe toroidally compactified string theory with twisted boundary conditions. In this theory fundamental particles are not pointlike and occupy a volume proportional to their R-charge. The theory breaks Lorentz invariance but appears to preserve spatial rotations. At low energies, it is approximately N=4 Super Yang-Mills theory, deformed by an operator of dimension seven. The dispersion relation of massless modes in vacuum is unchanged, but under certain conditions in this theory, particles can travel at superluminal velocities.
Toward a quantum theory of tachyon fields
NASA Astrophysics Data System (ADS)
Schwartz, Charles
2016-03-01
We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space-time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; Garcia-Ripoll, J. J.; Solano, E.
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Killing vector fields and harmonic superfield theories
Groeger, Josua
2014-09-15
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged
Coupling Constant Relations and Effective Lagrangian in the Type I Superstring
NASA Astrophysics Data System (ADS)
Sakai, N.; Abe, M.
1988-07-01
The relation between loop expansion parameters g_{op} for openstrings and g_{cl} for closed strings is explicitly determined inthe type I superstring with SO(N) gauge group (N=32 for theanomaly cancellation). This is translated to the relation between thegauge coupling constant g_YM and the gravitational couplingconstant kappa in the effective field theory Lagrangian. It isfound that the compactification on a torus with arbitrary shape andsize does not affect the relation.
New class of effective field theories from embedded branes.
Goon, Garrett L; Hinterbichler, Kurt; Trodden, Mark
2011-06-10
We present a new general class of four-dimensional effective field theories with interesting global symmetry groups. These theories arise from purely gravitational actions for (3+1)-dimensional branes embedded in higher dimensional spaces with induced gravity terms. The simplest example is the well known Galileon theory, with its associated Galilean symmetry, arising as the limit of a DGP brane world. However, we demonstrate that this is a special case of a much wider range of theories, with varying structures, but with the same attractive features such as second order equations. In some circumstances, these new effective field theories allow potentials for the scalar fields on curved space, with small masses protected by nonlinear symmetries. Such models may prove relevant to the cosmology of both the early and late universe. PMID:21770494
Heterotic/Type-II duality and its field theory avatars
Kiritsis, Elias
1999-10-25
In these lecture notes, I will describe heterotic/type-II duality in six and four dimensions. When supersymmetry is the maximal N=4 it will be shown that the duality reduces in the field theory limit to the Montonen-Olive duality of N=4 Super Yang-Mills theory. We will consider further compactifications of type II theory on Calabi-Yau manifolds. We will understand the physical meaning of geometric conifold singularities and the dynamics of conifold transitions. When the CY manifold is a K3 fibration we will argue that the type-II ground-state is dual to the heterotic theory compactified on K3xT{sup 2}. This allows an exact computation of the low effective action. Taking the field theory limit, {alpha}{sup '}{yields}0, we will recover the Seiberg-Witten non-perturbative solution of N=2 gauge theory.
Towards an effective field theory on the light-shell
NASA Astrophysics Data System (ADS)
Georgi, Howard; Kestin, Greg; Sajjad, Aqil
2016-03-01
We discuss our work toward the construction of a light-shell effective theory (LSET), an effective field theory for describing the matter emerging from high-energy collisions and the accompanying radiation. We work in the highly simplified venue of 0-flavor scalar quantum electrodynamics, with a gauge invariant product of scalar fields at the origin of space-time as the source of high-energy charged particles. Working in this simple gauge theory allows us to focus on the essential features of LSET. We describe how the effective theory is constructed and argue that it can reproduce the full theory tree-level amplitude. We study the 1-loop radiative corrections in the LSET and suggest how the leading double-logs in the full theory at 1-loop order can be reproduced by a purely angular integral in the LSET.
Conceptual Developments of 20th Century Field Theories
NASA Astrophysics Data System (ADS)
Cao, Tian Yu
1998-06-01
This volume provides a broad synthesis of conceptual developments of twentieth century field theories, from the general theory of relativity to quantum field theory and gauge theory. The book traces the foundations and evolution of these theories within a historio-critical context. Theoretical physicists and students of theoretical physics will find this a valuable account of the foundational problems of their discipline that will help them understand the internal logic and dynamics of theoretical physics. It will also provide professional historians and philosophers of science, particularly philosophers of physics, with a conceptual basis for further historical, cultural and sociological analysis of the theories discussed. Finally, the scientifically qualified general reader will find in this book a deeper analysis of contemporary conceptions of the physical world than can be found in popular accounts of the subject.
Conceptual Developments of 20th Century Field Theories
NASA Astrophysics Data System (ADS)
Cao, Tian Yu
1997-02-01
This volume provides a broad synthesis of conceptual developments of twentieth century field theories, from the general theory of relativity to quantum field theory and gauge theory. The book traces the foundations and evolution of these theories within a historio-critical context. Theoretical physicists and students of theoretical physics will find this a valuable account of the foundational problems of their discipline that will help them understand the internal logic and dynamics of theoretical physics. It will also provide professional historians and philosophers of science, particularly philosophers of physics, with a conceptual basis for further historical, cultural and sociological analysis of the theories discussed. Finally, the scientifically qualified general reader will find in this book a deeper analysis of contemporary conceptions of the physical world than can be found in popular accounts of the subject.
Topological Field Theory of Time-Reversal Invariant Insulators
Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
Dissipative Scalar Field Theory: A Covariant Formulation
NASA Astrophysics Data System (ADS)
Refaei, A.; Kheirandish, F.
2016-01-01
Caldeira-Leggett model of reservoir is generalized to a reservoir modeled by a continuum of real Klein-Gordon fields, instead of harmonic oscillators. A quantum Langevin type dissipative equation is obtained for the scalar field. The susceptibility of the medium is defined in terms of the reservoir Green's function and the coupling function satisfying causality condition. The connection between the coupling function and the susceptibility of the medium is found to be a Hankel transform from which the coupling function can be determined in terms of the susceptibility of the medium. Noise currents and their fluctuation-dissipation relation are obtained. In a homogeneous medium or reservoir, explicit form of the quantum scalar field, and its large-time limit, are found.
The Theory of Quantized Fields. III
DOE R&D Accomplishments Database
Schwinger, J.
1953-05-01
In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.
BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Mann, Robert
2013-02-01
Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons--kinks, vortices, and magnetic monopoles--and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is a tall order for a single chapter, relying rather heavily on additional background knowledge (for example supersymmetry) that students will not have unless they have already studied these topics in some depth. At this point students will need to be content with either appreciating the results as presented or else going to the original source material. The last four chapters of the book deal with anomalies and instantons, and again the reader is led from the simple material to the complex in a straightforward manner. Students should be able to follow the discussion both quantitatively and qualitatively, and become well-versed in understanding the 'big picture' provided they work through the material. The discussion on vacuum decay near the end of the book is quite timely given recent developments in eternal inflations, cosmic bubbles, and the like. The book contains a nice appendix that introduces students to the elements of Lie groups and Lie algebras that are required to understand a number of the ideas presented in various places in the book. There is also a short appendix on index theorems that should at least given students a basic sense of how these methods are employed in the subject at hand. This book would make a useful textbook for a mid-level graduate course. Though a bit terse in places, all of the main elements are there, in terms of both concept and methodology. It would make a fine addition to the library of any theorist in high-energy physics, gravitation, or cosmology.
On-Shell Recursion Relations for Effective Field Theories
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Shen, Chia-Hsien; Trnka, Jaroslav
2016-01-01
We derive the first ever on-shell recursion relations applicable to effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to construct all tree-level scattering amplitudes in the nonlinear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible.
Theory of back-surface-field solar cells
NASA Technical Reports Server (NTRS)
Vonroos, O.
1979-01-01
Report describes simple concise theory of back-surface-field (BSF) solar cells (npp + junctions) based on Shockley's depletion-layer approximation and cites superiority of two-junction devices over conventional unijunction cells.
The topological quantum field theory of Riemann's theta functions
NASA Astrophysics Data System (ADS)
Gelca, R?zvan; Hamilton, Alastair
2015-12-01
In this paper we prove the existence and uniqueness of a topological quantum field theory that incorporates, for all Riemann surfaces, the corresponding spaces of theta functions and the actions of the Heisenberg groups and modular groups on them.
Modeling pollutant transport using a meshless-lagrangian particle model
Carrington, D. B.; Pepper, D. W.
2002-01-01
A combined meshless-Lagrangian particle transport model is used to predict pollutant transport over irregular terrain. The numerical model for initializing the velocity field is based on a meshless approach utilizing multiquadrics established by Kansa. The Lagrangian particle transport technique uses a random walk procedure to depict the advection and dispersion of pollutants over any type of surface, including street and city canyons
Development of field theory in the last 50 years
Weisskopf, V.F.
1981-11-01
This article is devoted to the development of quantum field theory, a discipline that began with quantum electrodynamics which was born in 1927 when P. A. M. Dirac published his famous paper ''The Quantum Theory of the Emission and Absorption of Radiation.''
A Guided Inquiry Activity for Teaching Ligand Field Theory
ERIC Educational Resources Information Center
Johnson, Brian J.; Graham, Kate J.
2015-01-01
This paper will describe a guided inquiry activity for teaching ligand field theory. Previous research suggests the guided inquiry approach is highly effective for student learning. This activity familiarizes students with the key concepts of molecular orbital theory applied to coordination complexes. Students will learn to identify factors that…
A Guided Inquiry Activity for Teaching Ligand Field Theory
ERIC Educational Resources Information Center
Johnson, Brian J.; Graham, Kate J.
2015-01-01
This paper will describe a guided inquiry activity for teaching ligand field theory. Previous research suggests the guided inquiry approach is highly effective for student learning. This activity familiarizes students with the key concepts of molecular orbital theory applied to coordination complexes. Students will learn to identify factors that
Scalar field theory in {kappa}-Minkowski spacetime from twist
Kim, Hyeong-Chan; Lee, Youngone; Rim, Chaiho; Yee, Jae Hyung
2009-10-15
Using the twist deformation of U(igl(4,R)), the linear part of the diffeomorphism, we define a scalar function and construct a free scalar field theory in four-dimensional {kappa}-Minkowski spacetime. The action in momentum space turns out to differ only in the integration measure from the commutative theory.
Perturbation Theory of Massive Yang-Mills Fields
DOE R&D Accomplishments Database
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
An E6 gauge field theory model
NASA Astrophysics Data System (ADS)
Serdaroǧlu, Meral
1982-08-01
The standard and topless versions of a grand unified gauge model based on the exceptional group E6 are reviewed. Spontaneous symmetry breaking via Higgs fields transforming as the representations (27), (78) and (351) is discussed. Generation of Majorana masses for the right-handed neutrinos through analogues of Witten diagrams is shown to be compatible with the standard model.
Theory of a quantum noncanonical field in curved spacetimes
Indurain, Javier; Liberati, Stefano
2009-08-15
Much attention has been recently devoted to the possibility that quantum gravity effects could lead to departures from special relativity in the form of a deformed Poincare algebra. These proposals go generically under the name of doubly or deformed special relativity (DSR). In this article we further explore a recently proposed class of quantum field theories, involving noncanonically commuting complex scalar fields, which have been shown to entail a DSR-like symmetry. An open issue for such theories is whether the DSR-like symmetry has to be taken as a physically relevant symmetry, or if in fact the 'true' symmetries of the theory are just rotations and translations while boost invariance has to be considered broken. Here we analyze this issue by extending the known results to curved spacetime under both of the previous assumptions. We show that if the symmetry of the free theory is taken to be a DSR-like realization of the Poincare symmetry, then it is not possible to render such a symmetry a gauge symmetry of the curved physical spacetime. However, it is possible to introduce an auxiliary spacetime which allows one to describe the theory as a standard quantum field theory in curved spacetime. Alternatively, taking the point of view that the noncanonical commutation of the fields actually implies a breakdown of boost invariance, the physical spacetime manifold has to be foliated in surfaces of simultaneity, and the field theory can be coupled to gravity by making use of the Arnowitt-Deser-Misner prescription.
Effective field theory from modified gravity with massive modes
NASA Astrophysics Data System (ADS)
Capozziello, Salvatore; de Laurentis, Mariafelicia; Paolella, Mariacristina; Ricciardi, Giulia
2015-10-01
Massive gravitational modes in effective field theories can be recovered by extending General Relativity and taking into account generic functions of the curvature invariants, not necessarily linear in the Ricci scalar R. In particular, adopting the minimal extension of f(R) gravity, an effective field theory with massive modes is straightforwardly recovered. This approach allows to evade shortcomings like ghosts and discontinuities if a suitable choice of expansion parameters is performed.
On the Characters of Parafermionic Field Theories
NASA Astrophysics Data System (ADS)
Gepner, Doron
2015-06-01
We study cosets of the type H l / U(1) r , where H is any Lie algebra at level l and rank r. These theories are parafermionic and their characters are related to the string functions, which are generating functions for the multiplicities of weights in the affine representations. An identity for the characters is described, which apply to all the algebras and all the levels. The expression is of the Rogers-Ramanujan type. We verify this conjecture, for many algebras and levels, using Freudenthal-Kac formula, which calculates the multiplicities in the affine representations, recursively, up to some grade. Our conjecture encapsulates all the known results about these string functions, along with giving a vast wealth of new ones.
Radiation reaction in quantum field theory
NASA Astrophysics Data System (ADS)
Higuchi, Atsushi
2002-11-01
We investigate radiation-reaction effects for a charged scalar particle accelerated by an external potential realized as a space-dependent mass term in quantum electrodynamics. In particular, we calculate the position shift of the final-state wave packet of the charged particle due to radiation at lowest order in the fine structure constant α and in the small ħ approximation. We show that it disagrees with the result obtained using the Lorentz-Dirac formula for the radiation-reaction force, and that it agrees with the classical theory if one assumes that the particle loses its energy to radiation at each moment of time according to the Larmor formula in the static frame of the potential. However, the discrepancy is much smaller than the Compton wavelength of the particle. We also point out that the electromagnetic correction to the potential has no classical limit.
Light-front chiral effective field theory
Mathiot, J.-F.; Tsirova, N. A.
2013-11-15
We propose a general framework to calculate the nonperturbative structure of relativistic bound state systems. The state vector of the bound state is calculated in the covariant formulation of light-front dynamics. In this scheme, the state vector is defined on the light front of general position {omega} {center_dot} x = 0, where {omega} is an arbitrary light-like four-vector. This enables a strict control of any violation of rotational invariance. The state vector is then decomposed in Fock components. Our formalism is applied to the description of the nucleon properties at low energy, in chiral perturbation theory. We also show that the use of a recently proposed regularization scheme, the so-called Taylor-Lagrange regularization scheme, is very adequate in order to treat divergences in this nonperturbative framework.
Quantum theory for plasmon-assisted local field enhancement
NASA Astrophysics Data System (ADS)
Grigorenko, Ilya
2016-01-01
We applied quantum theory for nonlocal response and plasmon-assisted field enhancement near a small metallic nanoscale antenna in the limit of weak incoming fields. A simple asymmetric bio-inspired design of the nanoantenna for polarization-resolved measurement is proposed. The spatial field intensity distribution was calculated for different field frequencies and polarizations. We have shown that the proposed design the antenna allows us to resolve the polarization of incoming photons.
On the entanglement between interacting scalar field theories
NASA Astrophysics Data System (ADS)
Mozaffar, M. Reza Mohammadi; Mollabashi, Ali
2016-03-01
We study "field space entanglement" in certain quantum field theories consisting of N number of free scalar fields interacting with each other via kinetic mixing terms. We present exact analytic expressions for entanglement and Renyi entropies between arbitrary numbers of scalar fields by which we could explore certain entanglement inequalities. Other entanglement measures such as mutual information and entanglement negativity have also been studied. We also give some comments about possible holographic realizations of such models.
Effective hydrodynamic field theory and condensation picture of topological insulators
NASA Astrophysics Data System (ADS)
Chan, AtMa P. O.; Kvorning, Thomas; Ryu, Shinsei; Fradkin, Eduardo
2016-04-01
While many features of topological band insulators are commonly discussed at the level of single-particle electron wave functions, such as the gapless Dirac boundary spectrum, it remains elusive to develop a hydrodynamic or collective description of fermionic topological band insulators in 3+1 dimensions. As the Chern-Simons theory for the 2+1-dimensional quantum Hall effect, such a hydrodynamic effective field theory provides a universal description of topological band insulators, even in the presence of interactions, and that of putative fractional topological insulators. In this paper, we undertake this task by using the functional bosonization. The effective field theory in the functional bosonization is written in terms of a two-form gauge field, which couples to a U (1 ) gauge field that arises by gauging the continuous symmetry of the target system [the U (1 ) particle number conservation]. Integrating over the U (1 ) gauge field by using the electromagnetic duality, the resulting theory describes topological band insulators as a condensation phase of the U (1 ) gauge theory (or as a monopole condensation phase of the dual gauge field). The hydrodynamic description of the surface of topological insulators and the implication of its duality are also discussed. We also touch upon the hydrodynamic theory of fractional topological insulators by using the parton construction.
Free Quantum Field Theory from Quantum Cellular Automata
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Quantum field theory of interacting plasmon-photon-phonon system
NASA Astrophysics Data System (ADS)
Hieu Nguyen, Van; Nguyen, Bich Ha
2015-09-01
This work is devoted to the construction of the quantum field theory of the interacting system of plasmons, photons and phonons on the basis of general fundamental principles of electrodynamics and quantum field theory of many-body systems. Since a plasmon is a quasiparticle appearing as a resonance in the collective oscillation of the interacting electron gas in solids, the starting point is the total action functional of the interacting system comprising electron gas, electromagnetic field and phonon fields. By means of the powerful functional integral technique, this original total action is transformed into that of the system of the quantum fields describing plasmons, transverse photons, acoustic as well as optic longitudinal and transverse phonons. The collective oscillations of the electron gas is characterized by a real scalar field φ(x) called the collective oscillation field. This field is split into the static background field φ0(x) and the fluctuation field ζ(x). The longitudinal phonon fields {{{Q}}al}(x), {{{Q}}ol}(x) are also split into the background fields {Q}0al(x), {Q}0ol(x) and dynamical fields {{{q}}al}(x), {{{q}}ol}(x) while the transverse phonon fields {{{Q}}at}(x), {{{Q}}ot}(x) themselves are dynamical fields {{{q}}at}(x), {{{q}}ot}(x) without background fields. After the canonical quantization procedure, the background fields φ0(x), {Q}0al(x), {Q}0ol(x) remain the classical fields, while the fluctuation fields ζ(x) and dynamical phonon fields {{{q}}al}(x), {{{q}}at}(x), {{{q}}ol}(x), {{{q}}ot}(x) become quantum fields. In quantum theory, a plasmon is the quantum of Hermitian scalar field σ(x) called the plasmon field, longitudinal phonons as complex spinless quasiparticles are the quanta of the effective longitudinal phonon Hermitian scalar fields {{θ }a}(x), {{θ }0}(x), while transverse phonons are the quanta of the original Hermitian transverse phonon vector fields {{{q}}at}(x), {{{q}}ot}(x). By means of the functional integral technique the original action functional of the interacting system comprising electron gas, electromagnetic field and phonon fields is transformed into the total action functional of the resultant system comprising plasmon scalar quantum field σ(x), longitudinal phonon effective scalar quantum fields {{θ }a}(x), {{θ }0}(x) and transverse phonon vector quantum fields {{{q}}at}(x), {{{q}}ot}(x).
Conformal field theories with infinitely many conservation laws
Todorov, Ivan
2013-02-15
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, 'Unitary positive energy representations of scalar bilocal fields,' Commun. Math. Phys. 271, 223-246 (2007); e-print arXiv:math-ph/0604069v3; and 'Infinite dimensional Lie algebras in 4D conformal quantum field theory,' J. Phys. A Math Theor. 41, 194002 (2008); e-print arXiv:0711.0627v2 [hep-th
EULER-LAGRANGIAN COMPUTATIONS IN ESTUARINE HYDRODYNAMICS.
Cheng, Ralph T.
1983-01-01
The transport of conservative and suspended matter in fluid flows is a phenomenon of Lagrangian nature because the process is usually convection dominant. Nearly all numerical investigations of such problems use an Eulerian formulation for the convenience that the computational grids are fixed in space and because the vast majority of field data are collected in an Eulerian reference frame. Several examples are given in this paper to illustrate a modeling approach which combines the advantages of both the Eulerian and Lagrangian computational techniques.
Aspects of hadron and instanton physics in lattice quantum field theories
NASA Astrophysics Data System (ADS)
Pochinsky, Andrew
1997-10-01
An ongoing challenge to quantum chromodynamics as the theory of strong interactions is calculating hadron masses and matrix elements from first principles. Presently lattice calculations are the most promising means to probe low energy physics of quarks and gluons. The matrix element of the polarized on-shell nucleon state /langle ps/vert TJ/sbμ(x)J/sbν(0)/vert ps/rangle can be reduced to a set of spin-independent longitudinal and transverse structure functions Fi(x,/ Q2) and spin-dependent functions gi(x,/ Q2) and hi(x,/ Q2). Relevant matrix elements are calculated on a large lattice in the quenched approximation. In particular, the zeroth moment of the tensor charge is calculated for light valence quarks and extrapolated to the chiral limit. Topological excitations play an important role in nonperturbative quantum field theory. An introduction of the θ-term into the Lagrangian calls for special simulation techniques and sampling methods and requires a tremendous increase in statistics to get a signal. While QCD is still beyond current computational capabilities, investigations of simpler models will gain better understanding of topology related issues in lattice quantum field theories. The two dimensional O(3) σ-model with the θ-term is studied in the second part of the thesis. Using the cluster update algorithms and improved estimators a numerical check of Haldane's conjecture is performed. A special updating technique has been developed to construct an improved estimator for the topological charge and other observables to overcome the sign problem. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253- 1690.)
Abelian and nonabelian vector field effective actions from string field theory
NASA Astrophysics Data System (ADS)
Coletti, Erasmo; Sigalov, Ilya; Taylor, Washington
2003-09-01
The leading terms in the tree-level effective action for the massless fields of the bosonic open string are calculated by integrating out all massive fields in Witten's cubic string field theory. In both the abelian and nonabelian theories, field redefinitions make it possible to express the effective action in terms of the conventional field strength. The resulting actions reproduce the leading terms in the abelian and nonabelian Born-Infeld theories. In principle this method can be used to systematically determine all terms in the abelian and nonabelian actions, including all higher-order derivative terms.
Parallel computing using a Lagrangian formulation
NASA Technical Reports Server (NTRS)
Liou, May-Fun; Loh, Ching-Yuen
1992-01-01
This paper adopts a new Lagrangian formulation of the Euler equation for the calculation of two dimensional supersonic steady flow. The Lagrangian formulation represents the inherent parallelism of the flow field better than the common Eulerian formulation and offers a competitive alternative on parallel computers. The implementation of the Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, we have achieved better than six times speed-up on a 8192-processor CM-2 over a single processor of a CRAY-2.
Graphene, Lattice Field Theory and Symmetries
NASA Astrophysics Data System (ADS)
Drissi, L. B.; Saidi, E. H.; Bousmina, M.
2011-02-01
Borrowing ideas from tight binding model, we propose a board class of lattice field models that are classified by non simply laced Lie algebras. In the case of AN - 1 ≃ su(N) series, we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice L_{su( N) } are governed by the complex fundamental representations {{{\\underline N}}} and overline{{{N}}} of su(N) and the second nearest neighbor interactions are described by its adjoint {{ \\underline{{N}}}}⊗ overline{{{N}}}. The lattice models associated with the leading su(2), su(3), and su(4) cases are explicitly studied and their fermionic field realizations are given. It is also shown that the su(2) and su(3) models describe the electronic properties of the acetylene chain and the graphene, respectively. It is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the AN roots {α } through the typical dependence N/2+sum _{roots}cos ( {k}.α ) with {k} the wave vector. Other features such as the SO(2N) extension and other applications are also discussed.
Graphene, Lattice Field Theory and Symmetries
Drissi, L. B.; Bousmina, M.; Saidi, E. H.
2011-02-15
Borrowing ideas from tight binding model, we propose a board class of lattice field models that are classified by non simply laced Lie algebras. In the case of A{sub N-1{approx_equal}}su(N) series, we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice L{sub suN} are governed by the complex fundamental representations N-bar and N of su(N) and the second nearest neighbor interactions are described by its adjoint N-bar x N. The lattice models associated with the leading su(2), su(3), and su(4) cases are explicitly studied and their fermionic field realizations are given. It is also shown that the su(2) and su(3) models describe the electronic properties of the acetylene chain and the graphene, respectively. It is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the A{sub N} roots {alpha} through the typical dependence N/2+{Sigma}{sub roots} cos(k.{alpha} with k the wave vector.Other features such as the SO(2N) extension and other applications are also discussed.
Generating functionals for quantum field theories with random potentials
NASA Astrophysics Data System (ADS)
Jain, Mudit; Vanchurin, Vitaly
2016-01-01
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include cosmological systems in context of the string theory landscape (e.g. cosmic inflation) or condensed matter systems with quenched disorder (e.g. spin glass). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out and in-in correlators and the replica limits are taken to only a zero number of fields. We discuss the formalism in details for a single real scalar field, but the generalization to more fields or to different types of fields is straightforward. We work out three examples: one where the mass of scalar field is treated as a random variable and two where the functional form of interactions is random, one described by a Gaussian random field and the other by a Euclidean action in the field configuration space.
Topics in lattice QCD and effective field theory
NASA Astrophysics Data System (ADS)
Buchoff, Michael I.
Quantum Chromodynamics (QCD) is the fundamental theory that governs hadronic physics. However, due to its non-perturbative nature at low-energy/long distances, QCD calculations are difficult. The only method for performing these calculations is through lattice QCD. These computationally intensive calculations approximate continuum physics with a discretized lattice in order to extract hadronic phenomena from first principles. However, as in any approximation, there are multiple systematic errors between lattice QCD calculation and actual hardronic phenomena. Developing analytic formulae describing the systematic errors due to the discrete lattice spacings is the main focus of this work. To account for these systematic effects in terms of hadronic interactions, effective field theory proves to be useful. Effective field theory (EFT) provides a formalism for categorizing low-energy effects of a high-energy fundamental theory as long as there is a significant separation in scales. An example of this is in chiral perturbation theory (chiPT), where the low-energy effects of QCD are contained in a mesonic theory whose applicability is a result of a pion mass smaller than the chiral breaking scale. In a similar way, lattice chiPT accounts for the low-energy effects of lattice QCD, where a small lattice spacing acts the same way as the quark mass. In this work, the basics of this process are outlined, and multiple original calculations are presented: effective field theory for anisotropic lattices, I=2 pipi scattering for isotropic, anisotropic, and twisted mass lattices. Additionally, a combination of effective field theory and an isospin chemical potential on the lattice is proposed to extract several computationally difficult scattering parameters. Lastly, recently proposed local, chiral lattice actions are analyzed in the framework of effective field theory, which illuminates various challenges in simulating such actions.
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1993-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. The present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multidimensional discontinuities with a high level of accuracy, similar to that found in 1D problems.
Gravity, Time, and Lagrangians
ERIC Educational Resources Information Center
Huggins, Elisha
2010-01-01
Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…
Some equivalences between the auxiliary field method and envelope theory
Buisseret, Fabien; Semay, Claude; Silvestre-Brac, Bernard
2009-03-15
The auxiliary field method has been recently proposed as an efficient technique to compute analytical approximate solutions of eigenequations in quantum mechanics. We show that the auxiliary field method is completely equivalent to the envelope theory, which is another well-known procedure to analytically solve eigenequations, although relying on different principles a priori. This equivalence leads to a deeper understanding of both frameworks.
3D Quantum Gravity and Effective Noncommutative Quantum Field Theory
Freidel, Laurent; Livine, Etera R.
2006-06-09
We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a {kappa} deformation of the Poincare group.
Medical Argument and Field Theory: The Laetrile Case.
ERIC Educational Resources Information Center
Dunbar, Nancy R.
One approach to field theory in argumentation begins with a description of argumentation and, by identifying similarities or regularities in discursive practice, attempts to induce the nature and characteristics of a field. The controversy surrounding the use of Laetrile, a proposed cancer treatment, provides an example of this approach. Assuming…
Long-range interactions in lattice field theory
Rabin, J.M.
1981-06-01
Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.
Hermeneutical Field Theory and the Structural Character of Understanding.
NASA Astrophysics Data System (ADS)
Whitehouse, William Leonard
Through a series of exploratory case studies focusing on hermeneutics, phenomenology, relativity, field theory, quantum mechanics, chronobiology, chaos theory, holographic theory and various aspects of mathematics, a set of hermeneutical constraints and degrees of freedom are generated. There are a set of eight field equations given in the thesis which give qualitative symbolic expression to the aforementioned spectrum of constraints and degrees of freedom that constitute the structural character of understanding. However, as is sometimes the case with their quantitative mathematical counterparts, the hermeneutical field equations are capable of giving a variety of descriptions or solutions for one and the same set of conditions. The task, therefore, is to try to sort out those solutions which have reflective properties with respect to the structural character of reality from those which do not have such properties. The thesis addresses this task by introducing the idea of hermeneutical field theory. In this theory the notion of a semiotic operator or semiotic quantum plays a central role. More specifically, this quantum is considered to be the carrier of hermeneutical force. It arises as a field property at the complex, horizontal membrane-manifold linking human consciousness with different levels of scale of reality. When taken collectively, the aforementioned set of equations gives expression to the structural character of hermeneutical field theory. Therefore, when one begins to run concrete variables through the theory underlying these equations, one encounters various kinds of hermeneutical constraints and degrees of freedom. These constraints and degrees of freedom characterize the dialectical engagement of consciousness and reality as one seeks to acquire understanding concerning the above mentioned variables and the context which gives rise to them. Hermeneutical field theory is really the study of the factors that affect the state of the six internal 'spin' components of the semiotic quantum (i.e., identifying reference, reflexive consciousness, characterization, the interrogative imperative, inferential mapping, and congruence functions) in any given instance of dialectical interaction between consciousness and reality. Consequently, on the one hand, hermeneutical field theory involves an investigation of the potential sources of curvature or distortion which may be introduced into the exchange or transduction process occurring during the dialectical engagement between consciousness and reality. On the other hand, hermeneutical field theory is a study of the factors which need to be taken into consideration to establish hermeneutical point-structures, neighborhoods or latticeworks which can serve as analogs for different aspects of reality toward which attention is being directed. (Abstract shortened by UMI.).
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1995-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.
Toward classical geometrodynamics from the group field theory hydrodynamics
NASA Astrophysics Data System (ADS)
Oriti, Daniele; Sindoni, Lorenzo
2011-02-01
We take the first steps toward identifying the hydrodynamics of group field theories (GFTs) and relating this hydrodynamic regime to the classical geometrodynamics of continuum space. We apply to GFT mean field theory techniques borrowed from the theory of Bose condensates, alongside standard GFT and spin foam techniques. The mean field configuration we study is, in turn, obtained from loop quantum gravity coherent states. We work in the context of two-dimensional (2D) and 3D GFT models, in Euclidean signature, both ordinary and colored, as examples of a procedure that has a more general validity. We also extract the effective dynamics of the system around the mean field configurations, and discuss the role of GFT symmetries in going from microscopic to effective dynamics. In the process, we obtain additional insights into the GFT formalism itself.
Generalized conservation laws in non-local field theories
NASA Astrophysics Data System (ADS)
Kegeles, Alexander; Oriti, Daniele
2016-04-01
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalized conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalization of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
Prime Numbers, Quantum Field Theory and the Goldbach Conjecture
NASA Astrophysics Data System (ADS)
Sanchis-Lozano, Miguel-Angel; Barbero G., J. Fernando; Navarro-Salas, José
2012-09-01
Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space-time, we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators bp\\dag — labeled by prime numbers p — acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allows us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.
Non-Abelian fluid dynamics in Lagrangian formulation
NASA Astrophysics Data System (ADS)
Bistrovic, B.; Jackiw, R.; Li, H.; Nair, V. P.; Pi, S.-Y.
2003-01-01
Non-Abelian extensions of fluid dynamics, which can have applications to the quark-gluon plasma, are given. These theories are presented in a symplectic or Lagrangian formulation and involve a fluid generalization of the Kirillov-Kostant form well known in Lie group theory. In our simplest model the fluid flows with velocity v and, in the presence of non-Abelian chromoelectric or magnetic Ea/Ba fields, the fluid feels a Lorentz force of the form QaEa+(v/c)×QaBa, where Qa is a space-time local non-Abelian charge satisfying a fluid Wong equation [(Dt+vṡD)Q]a=0 with gauge covariant derivatives.
Janiszewski, Stefan; Karch, Andreas
2013-02-22
We argue that generic nonrelativistic quantum field theories with a holographic description are dual to Hořava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a nonrelativistic scaling limit. PMID:23473127
Quantum field theory constrains traversable wormhole geometries
Ford, L.H.; Roman, T.A.
1996-05-01
Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty-principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable. {copyright} {ital 1996 The American Physical Society.}
Warped conformal field theory as lower spin gravity
NASA Astrophysics Data System (ADS)
Hofman, Diego M.; Rollier, Blaise
2015-08-01
Two dimensional Warped Conformal Field Theories (WCFTs) may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non-AdS space-times, including the near horizon geometry of generic extremal black holes. It is shown in this paper that WCFTs posses a type of boost symmetry. Using this insight, we discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton-Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories is presented and we write two explicit examples of WCFTs. These are free fermionic theories. Lastly we present a systematic description of the holographic duals of WCFTs. It is argued that the minimal setup is not Einstein gravity but an SL (2, R) × U (1) Chern-Simons Theory, which we call Lower Spin Gravity. This point of view makes manifest the definition of boundary for these non-AdS geometries. This case represents the first step towards understanding a fully invariant formalism for WN field theories and their holographic duals.
Quantum Field Theory in Curved Spacetime
NASA Astrophysics Data System (ADS)
Reynolds, Sally C.; Gallagher, Andrew
2012-03-01
List of contributors; Foreword J. T. Francis Thackeray; 1. African genesis: an evolving paradigm Sally C. Reynolds; 2. Academic genealogy Peter Ungar and Phillip V. Tobias; Part I. In Search of Origins: Evolutionary Theory, New Species, and Paths into the Past: 3. Speciation in hominin evolution Colin Groves; 4. Searching for a new paradigm for hominid origins in Chad (Central Africa) Michel Brunet; 5. From hominoid arboreality to hominid bipedalism Brigitte Senut; 6. Orrorin and the African ape/hominid dichotomy Martin Pickford; 7. A brief history and results of 40 years of Sterkfontein excavations Ronald J. Clarke; Part II. Hominin Morphology Through Time: Brains, Bodies and Teeth: 8. Hominin brain evolution, 1925-2011: an emerging overview Dean Falk; 9. The issue of brain reorganisation in Australopithecus and early hominids: Dart had it right Ralph L. Holloway; 10. The mass of the human brain: is it a spandrel? Paul R. Manger, Jason Hemingway, Muhammad Spocter and Andrew Gallagher; 11. Origin and diversity of early hominin bipedalism Henry M. McHenry; 12. Forelimb adaptations in Australopithecus afarensis Michelle S. M. Drapeau; 13. Hominin proximal femur morphology from the Tugen Hills to Flores Brian G. Richmond and William L. Jungers; 14. Daily rates of dentine formation and root extension rates in Paranthropus boisei, KNM-ER 1817, from Koobi Fora, Kenya M. Christopher Dean; 15. On the evolutionary development of early hominid molar teeth and the Gondolin Paranthropus molar Kevin L. Kuykendall; 16. Digital South African fossils: morphological studies using reference-based reconstruction and electronic preparation Gerhard W. Weber, Philipp Gunz, Simon Neubauer, Philipp Mitteroecker and Fred L. Bookstein; Part III. Modern Human Origins: Patterns, and Processes: 17. Body size in African Middle Pleistocene Homo Steven E. Churchill, Lee R. Berger, Adam Hartstone-Rose and Headman Zondo; 18. The African origin of recent humanity Milford H. Wolpoff and Sang-Hee Lee; 19. Assimilation and modern human origins in the African peripheries Fred H. Smith, Vance T. Hutchinson and Ivor Janković; 20. Patterns of Middle Pleistocene hominin evolution in Africa and the emergence of modern humans Emma Mbua and Günter Bräuer; 21. Integration of the genetic, anatomical, and archaeological data for the African origin of modern humans: problems and prospects Osbjorn M. Pearson; Part IV. In Search of Context: Hominin Environments, Behaviour and Lithic Cultures: 22. Animal palaeocommunity variability and habitat preference of robust australopiths in South Africa Darryl J. de Ruiter, Matt Sponheimer and Julia Lee-Thorp; 23. Impacts of environmental change and community ecology on the composition and diversity of the southern African monkey fauna from the Plio-Pleistocene to the present Sarah Elton; 24. African genesis revisited: reflections on Raymond Dart and the 'Predatory Transition from Ape(-Man) to Man' Travis R. Pickering; 25. Shared intention in early artefacts: an exploration of deep structure and implications for communication and language John A. J. Gowlett; 26. Sibudu Cave: recent archaeological work on the Middle Stone Age Lyn Wadley; 27. The oldest burials and their significance Avraham Ronen; Index.
Massive basketball diagram for a thermal scalar field theory
NASA Astrophysics Data System (ADS)
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-01
The ``basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a φ4 interaction to three-loop order.
Coupled Mesh Lagrangian/ALE modeling: opportunities and challenges.
Wong, Michael K. W.; Voth, Thomas Eugene; Hensinger, David M.; Bishop, Joseph E.; Robinson, Allen Conrad
2005-06-01
The success of Lagrangian contact modeling leads one to believe that important aspects of this capability may be used for multi-material modeling when only a portion of the simulation can be represented in a Lagrangian frame. We review current experience with two dual mesh technologies where one of these meshes is a Lagrangian mesh and the other is an Arbitrary Lagrangian/Eulerian (ALE) mesh. These methods are cast in the framework of an operator-split ALE algorithm where a Lagrangian step is followed by a remesh/remap step. An interface-coupled methodology is considered first. This technique is applicable to problems involving contact between materials of dissimilar compliance. The technique models the more compliant (soft) material as ALE while the less compliant (hard) material and associated interface are modeled in a Lagrangian fashion. Loads are transferred between the hard and soft materials via explicit transient dynamics contact algorithms. The use of these contact algorithms remove the requirement of node-tonode matching at the soft-hard interface. In the context of the operator-split ALE algorithm, a single Lagrangian step is performed using a mesh to mesh contact algorithm. At the end of the Lagrangian step the meshes will be slightly offset at the interface but non-interpenetrating. The ALE mesh nodes at the interface are then remeshed to their initial location relative to the Lagrangian body faces and the ALE mesh is smoothed, translated and rotated to follow Lagrangian body. Robust remeshing in the ALE region is required for success of this algorithm, and we describe current work in this area. The second method is an overlapping grid methodology that requires mapping of information between a Lagrangian mesh and an ALE mesh. The Lagrangian mesh describes a relatively hard body that interacts with softer material contained in the ALE mesh. A predicted solution for the velocity field is performed independently on both meshes. Element-centered velocity and momentum are transferred between the meshes using the volume transfer capability implemented in contact algorithms. Data from the ALE mesh is mapped to a phantom mesh that surrounds the Lagrangian mesh, providing for the reaction to the predicted motion of the Lagrangian material. Data from the Lagrangian mesh is mapped directly to the ALE mesh. A momentum balance is performed on both meshes to adjust the velocity field to account for the interaction of the material from the other mesh. Subsequent, remeshing and remapping of the ALE mesh is performed to allow large deformation of the softer material. We overview current progress using this approach and discuss avenues for future research and development.
Entanglement entropy in scalar field theory on the fuzzy sphere
NASA Astrophysics Data System (ADS)
Okuno, Shizuka; Suzuki, Mariko; Tsuchiya, Asato
2016-02-01
We study entanglement entropy on the fuzzy sphere. We calculate it in a scalar field theory on the fuzzy sphere, which is given by a matrix model. We use a method that is based on the replica method and applicable to interacting fields as well as free fields. For free fields, we obtain results consistent with the previous study, which serves as a test of the validity of the method. For interacting fields, we perform Monte Carlo simulations at strong coupling and see a novel behavior of entanglement entropy.
Bound states in Galilean-invariant quantum field theory
Corley, S.R.; Greenberg, O.W.
1997-02-01
We consider the nonrelativistic quantum mechanics of a model of two spinless fermions interacting via a two-body potential. We introduce quantum fields associated with the two particles as well as the expansion of these fields in asymptotic {open_quotes}in{close_quotes} and {open_quotes}out{close_quotes} fields, including such fields for bound states, in principle. We limit our explicit discussion to a two-body bound state. In this context we discuss the implications of the Galilean invariance of the model and, in particular, show how to include bound states in a strictly Galilean-invariant quantum field theory. {copyright} {ital 1997 American Institute of Physics.}
Thermofield dynamics extension of the open string field theory
NASA Astrophysics Data System (ADS)
Botta Cantcheff, M.; Scherer Santos, R. J.
2016-03-01
We study the application of the rules of thermofield dynamics (TFD) to the covariant formulation of open-string field theory. We extend the states space and fields according to the duplication rules of TFD and construct the corresponding classical action. The result is interpreted as a theory whose fields would encode the statistical information of open strings. The physical spectrum of the free theory is studied through the cohomology of the extended Becchi, Rouet, Stora and Tyutin (BRST) charge, and, as a result, we get new fields in the spectrum emerging by virtue of the quantum entanglement, and, noticeably, it presents degrees of freedom that could be identified as those of closed strings. We also show, however, that their appearing in the action is directly related to the choice of the inner product in the extended algebra, so that different sectors of fields could be eliminated from the theory by choosing that product conveniently. Finally, we study the extension of the three-vertex interaction and provide a simple prescription for it of which the results at tree level agree with those of the conventional theory.
Observations on the moduli space of superconformal field theories
NASA Astrophysics Data System (ADS)
Seiberg, Nathan
1988-06-01
Some aspects of the moduli space of superconformal field theories are discussed. It is helpful to consider the conformal field theory as a background for propagation of strings and to exploit the space-time interpretation. Using this point of view we show that the metric on the moduli space of N = 4 superconformal field theory with c = 6 is locally that of O(20,4)/O(20) × O(4). We also discover some properties of the moduli space of N = 2 superconformal field theories with c = 9. Particular examples of these conformal field theories are sigma models on four- and six-dimensional Calabi-Yau spaces. Therefore, we can use this technique to learn about the moduli space of these spaces. For c = 6 we recover the known moduli space of K 3. Our analysis of the c = 9 system leads to a new coupling in four dimensional supergravity. As a by-product, we prove that gauge couplings cannot depend on the moduli of N = 1 space-time supersymmetric compactifications.
Possibility of gravitational quantization under the teleparallel theory of gravitation
NASA Astrophysics Data System (ADS)
Ming, Kian; Triyanta, Kosasih, J. S.
2016-03-01
Teleparallel gravity (TG) or tele-equivalent general relativity (TEGR) is an alternative gauge theory for gravity. In TG tetrad fields are defined to express gravitational fields and act like gauge potentials in standard gauge theory. The lagrangians for the gravitational field in TG and for the Yang-Mills field in standard gauge theory differ due to different indices that stick on the components of the corresponding fields: two external indices for tetrad field and internal and external indices for the Yang-Mills field. Different types of indices lead to different possible contractions and thus lead to different expression of the lagrangian for the Yang Mills field and for the tetrad field. As TG is a gauge theory it is then natural to quantize gravity in TG by applying the same procedure of quantization as in the standard gauge theory. Here we will discuss on the possibility to quantize gravity, canonically and functionally, under the framework of TG theory.
Consistent constraints on the Standard Model Effective Field Theory
NASA Astrophysics Data System (ADS)
Berthier, Laure; Trott, Michael
2016-02-01
We develop the global constraint picture in the (linear) effective field theory generalisation of the Standard Model, incorporating data from detectors that operated at PEP, PETRA, TRISTAN, SpS, Tevatron, SLAC, LEPI and LEP II, as well as low energy precision data. We fit one hundred and three observables. We develop a theory error metric for this effective field theory, which is required when constraints on parameters at leading order in the power counting are to be pushed to the percent level, or beyond, unless the cut off scale is assumed to be large, Λ ≳ 3 TeV. We more consistently incorporate theoretical errors in this work, avoiding this assumption, and as a direct consequence bounds on some leading parameters are relaxed. We show how an S, T analysis is modified by the theory errors we include as an illustrative example.
Chiral Effective Field Theory in the $\\Delta$-resonance region
Vladimir Pascalutsa
2006-09-18
I discuss the problem of constructing an effective low-energy theory in the vicinity of a resonance or a bound state. The focus is on the example of the $\\Delta(1232)$, the lightest resonance in the nucleon sector. Recent developments of the chiral effective-field theory in the $\\Delta$-resonance region are briefly reviewed. I conclude with a comment on the merits of the manifestly covariant formulation of chiral EFT in the baryon sector.
Quantum field theory on curved spacetimes: Axiomatic framework and examples
NASA Astrophysics Data System (ADS)
Fredenhagen, Klaus; Rejzner, Kasia
2016-03-01
In this review article, we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an almost self-contained introduction into the framework, which should be accessible for both mathematical physicists and mathematicians.
Large field inflation models from higher-dimensional gauge theories
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-23
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante’s Inferno model turns out to be the most preferred model in this framework.
Regularization methods for Nuclear Lattice Effective Field Theory
NASA Astrophysics Data System (ADS)
Klein, Nico; Lee, Dean; Liu, Weitao; Meißner, Ulf-G.
2015-07-01
We investigate Nuclear Lattice Effective Field Theory for the two-body system for several lattice spacings at lowest order in the pionless as well as in the pionful theory. We discuss issues of regularizations and predictions for the effective range expansion. In the pionless case, a simple Gaussian smearing allows to demonstrate lattice spacing independence over a wide range of lattice spacings. We show that regularization methods known from the continuum formulation are necessary as well as feasible for the pionful approach.
Effective-field theory on the kinetic Ising model
NASA Astrophysics Data System (ADS)
Shi, Xiaoling; Wei, Guozhu; Li, Lin
2008-09-01
As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the square lattice (Z=4) and the simple cubic lattice (Z=6), respectively. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. In the field amplitude h/ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn, and the dynamical tricritical point has been observed. We also make the compare results of EFT with that given by using the mean field theory (MFT).
Quantum field theory in spaces with closed timelike curves
NASA Astrophysics Data System (ADS)
Boulware, David G.
1992-11-01
Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Lagrangian simulation of Taylor-Couette flow
NASA Astrophysics Data System (ADS)
Emery, M. H.; Fritts, M. J.; Shockley, R. C.
1981-07-01
We report on the development of a hydrodynamics code designed for the Lagrangian simulation of transient rotational flow phenomena. The code solves the incompressible, inviscid fluid equations in an axisymmetric, cylindrical coordinate system. The equations of motion are finite differenced on a general connectivity triangular mesh. Here we apply the model to the study of the transition from laminar Couette flow to Taylor vortex flow and obtain very good agreement with the linear theory.
Lagrangian generators of the Poincare gauge symmetries
Banerjee, Rabin; Roy, Debraj; Samanta, Saurav
2010-08-15
We have systematically computed the generators of the symmetries arising in Poincare gauge theory formulation of gravity, both in 2+1 and 3+1 dimensions. This was done using a completely Lagrangian approach. The results are expected to be valid in any dimensions, as seen through lifting the results of the 2+1 dimensional example into the 3+1 dimensional one.
Lagrangian based methods for coherent structure detection
NASA Astrophysics Data System (ADS)
Allshouse, Michael R.; Peacock, Thomas
2015-09-01
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows.
Lagrangian based methods for coherent structure detection
Allshouse, Michael R.; Peacock, Thomas
2015-09-15
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows.
Lagrangian based methods for coherent structure detection.
Allshouse, Michael R; Peacock, Thomas
2015-09-01
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows. PMID:26428570
A Variational Statistical-Field Theory for Polar Liquid Mixtures
NASA Astrophysics Data System (ADS)
Zhuang, Bilin; Wang, Zhen-Gang
Using a variational field-theoretic approach, we derive a molecularly-based theory for polar liquid mixtures. The resulting theory consists of simple algebraic expressions for the free energy of mixing and the dielectric constant as functions of mixture composition. Using only the dielectric constants and the molar volumes of the pure liquid constituents, the theory evaluates the mixture dielectric constants in good agreement with the experimental values for a wide range of liquid mixtures, without using adjustable parameters. In addition, the theory predicts that liquids with similar dielectric constants and molar volumes dissolve well in each other, while sufficient disparity in these parameters result in phase separation. The calculated miscibility map on the dielectric constant-molar volume axes agrees well with known experimental observations for a large number of liquid pairs. Thus the theory provides a quantification for the well-known empirical ``like-dissolves-like'' rule. Bz acknowledges the A-STAR fellowship for the financial support.
Continuous-spin particle field theory with helicity correspondence
NASA Astrophysics Data System (ADS)
Schuster, Philip; Toro, Natalia
2015-01-01
We propose the first covariant local action describing the propagation of a single free continuous-spin degree of freedom. The theory is simply formulated as a gauge theory in a "vector superspace," but can also be formulated in terms of a tower of symmetric tensor gauge fields. When the spin invariant ρ vanishes, the helicity correspondence is manifest—familiar gauge theory actions are recovered and couplings to conserved currents can easily be introduced. For nonzero ρ , a tower of tensor currents must be present, of which only the lowest rank is exactly conserved. A paucity of local gauge-invariant operators for nonzero ρ suggests that the equations of motion in any interacting theory should be covariant, not invariant, under a generalization of the free theory's gauge symmetry.
Negative-frequency modes in quantum field theory
NASA Astrophysics Data System (ADS)
Dickinson, Robert; Forshaw, Jeff; Millington, Peter
2015-07-01
We consider a departure from standard quantum field theory, constructed so as to permit momentum eigenstates of both positive and negative energy. The resulting theory is intriguing because it brings about the cancellation of leading ultra-violet divergences and the absence of a zero-point energy. The theory gives rise to tree-level source-to-source transition amplitudes that are manifestly causal and consistent with standard S-matrix elements. It also leads to the usual result for the oblique corrections to the standard electroweak theory. Remarkably, the latter agreement relies on the breakdown of naive perturbation theory due to resonance effects. It remains to be shown that there are no problems with perturbative unitarity.
Constructing the Lagrangian in the Eulerian coordinate for relativistic hydrodynamics
NASA Astrophysics Data System (ADS)
Chiueh, Tzihong
1994-02-01
The Lorentz-covariant Lagrangian for an ideal relativistic flow is constructed in the Eulerian coordinate. In contrast to the Lagrangian of nonrelativistic flows in the Eulerian formulation, for which the continuity equation is required to be externally imposed as a constraint [Mittag, Stephen, and Yourgrau, in Variational Principles in Dynamics .ul and Quantum Theory, edited by W. Yourgrau and X. Mandelstam (Dover, New York, 1968)], this Lorentz-covariant Lagrangian automatically yields the continuity equation as well as the equation of state. In addition, the relativistic generalization of the Bernoulli equation can also be derived from the present formulation.
Hierarchy of effective field theories of hot electroweak matter
NASA Astrophysics Data System (ADS)
Jakovác, A.; Kajantie, K.; Patkós, A.
1994-06-01
A hierarchy of effective three-dimensional theories of finite temperature electroweak matter is studied. First an integration over nonstatic modes leads to an effective theory containing a gauge field Aai, an adjoint Higgs field Aa0, and the fundamental Higgs field φα. We carry out the integration in the one-loop approximation, study renormalization effects, and estimate quantitatively those terms of the effective action which are suppressed by inverse powers of the temperature. Second, because of the existence of well-separated thermal mass scales, Aa0 can be integrated over, and finally also φα, leaving an effective theory of the Aai. In the analysis of the subsequent models particular attention is paid to the screening of the magnetic fluctuations due to the integrated-out degrees of freedom.
Scaling behavior of three-dimensional group field theory
NASA Astrophysics Data System (ADS)
Magnen, Jacques; Noui, Karim; Rivasseau, Vincent; Smerlak, Matteo
2009-09-01
Group field theory is a generalization of matrix models, with triangulated pseudomanifolds as Feynman diagrams and state sum invariants as Feynman amplitudes. In this paper, we consider Boulatov's three-dimensional model and its Freidel-Louapre positive regularization (hereafter the BFL model) with an 'ultraviolet' cutoff, and study rigorously their scaling behavior in the large cutoff limit. We prove an optimal bound on large order Feynman amplitudes, which shows that the BFL model is perturbatively more divergent than the former. We then upgrade this result to the constructive level, using, in a self-contained way, the modern tools of constructive field theory: we construct the Borel sum of the BFL perturbative series via a convergent 'cactus' expansion, and establish the 'ultraviolet' scaling of its Borel radius. Our method shows how the 'sum over triangulations' in quantum gravity can be tamed rigorously, and paves the way for the renormalization program in group field theory.
Noncausal propagation in spin-0 theories with external field interactions
NASA Technical Reports Server (NTRS)
Guertin, R. F.; Wilson, T. L.
1977-01-01
The two-component Sakata-Taketani (ST) spin-0 theory and the single-component Klein-Gordon theory are obtained from the five-component Duffin-Kemmer-Petiau (DKP) theory with six types of external field interactions by means of a Peirce decomposition. Whereas the DKP equation manifests the covariance, the ST equation manifests the causal properties. In particular, the presence of noncausal wave propagation when there is coupling to a second-rank tensor field is apparent from the form of the ST equation, in which the coefficients of all the space derivatives depend on the external field. The results indicate that the causal properties of higher-spin equations should also be obvious when they are expressed in 2(2J + 1)-component Schroedinger form
Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
NASA Astrophysics Data System (ADS)
Schenkel, Alexander
2012-10-01
The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to noncommutative gravity. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models. In part two we develop a new formalism for quantum field theory on noncommutative curved spacetimes by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. We also study explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories. The convergent deformation of simple toy models is investigated and it is found that these theories have an improved behaviour at short distances, i.e. in the ultraviolet. In part three we study homomorphisms between and connections on noncommutative vector bundles. We prove that all homomorphisms and connections of the deformed theory can be obtained by applying a quantization isomorphism to undeformed homomorphisms and connections. The extension of homomorphisms and connections to tensor products of bimodules is clarified. As a nontrivial application of the new mathematical formalism we extend our studies of exact noncommutative gravity solutions to more general deformations.
BPS Quivers and Spectra of Complete Quantum Field Theories
NASA Astrophysics Data System (ADS)
Alim, Murad; Cecotti, Sergio; Córdova, Clay; Espahbodi, Sam; Rastogi, Ashwin; Vafa, Cumrun
2013-11-01
We study the BPS spectra of complete quantum field theories in four dimensions. For examples that can be described by a pair of M5 branes on a punctured Riemann surface we explain how triangulations of the surface fix a BPS quiver and superpotential for the theory. The BPS spectrum can then be determined by solving the quantum mechanics problem encoded by the quiver. By analyzing the structure of this quantum mechanics we show that all asymptotically free examples, Argyres-Douglas models, and theories defined by punctured spheres and tori have a chamber with finitely many BPS states. In all such cases we determine the spectrum.
Chaotic Lagrangian transport and mixing in the ocean
NASA Astrophysics Data System (ADS)
Prants, S. V.
2014-12-01
Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean. The basic theoretical ideas have been borrowed from the phenomenon of chaotic advection in fluids, an analogue of dynamical Hamiltonian chaos in mechanics. The starting point for analysis is a velocity field obtained by this or that way. Being motivated by successful applications of that approach to simplified analytic models of geophysical fluid flows, researchers now work with satellite-derived velocity fields and outputs of sophisticated numerical models of ocean circulation. This review article gives an introduction to some of the basic concepts and methods used to study chaotic mixing and transport in the ocean and a brief overview of recent results with some practical applications of Lagrangian tools to monitor spreading of Fukushima-derived radionuclides in the ocean.
New Phenomena in NC Field Theory and Emergent Spacetime Geometry
NASA Astrophysics Data System (ADS)
Ydri, Badis
2010-10-01
We give a brief review of two nonperturbative phenomena typical of noncommutative field theory which are known to lead to the perturbative instability known as the UV-IR mixing. The first phenomena concerns the emergence/evaporation of spacetime geometry in matrix models which describe perturbative noncommutative gauge theory on fuzzy backgrounds. In particular we show that the transition from a geometrical background to a matrix phase makes the description of noncommutative gauge theory in terms of fields via the Weyl map only valid below a critical value g*. The second phenomena concerns the appearance of a nonuniform ordered phase in noncommutative scalar φ4 field theory and the spontaneous symmetry breaking of translational/rotational invariance which happens even in two dimensions. We argue that this phenomena also originates in the underlying matrix degrees of freedom of the noncommutative field theory. Furthermore it is conjectured that in addition to the usual WF fixed point at θ = 0 there must exist a novel fixed point at θ = ∞ corresponding to the quartic hermitian matrix model.
New Phenomena in NC Field Theory and Emergent Spacetime Geometry
Ydri, Badis
2010-10-31
We give a brief review of two nonperturbative phenomena typical of noncommutative field theory which are known to lead to the perturbative instability known as the UV-IR mixing. The first phenomena concerns the emergence/evaporation of spacetime geometry in matrix models which describe perturbative noncommutative gauge theory on fuzzy backgrounds. In particular we show that the transition from a geometrical background to a matrix phase makes the description of noncommutative gauge theory in terms of fields via the Weyl map only valid below a critical value g*. The second phenomena concerns the appearance of a nonuniform ordered phase in noncommutative scalar {phi}{sup 4} field theory and the spontaneous symmetry breaking of translational/rotational invariance which happens even in two dimensions. We argue that this phenomena also originates in the underlying matrix degrees of freedom of the noncommutative field theory. Furthermore it is conjectured that in addition to the usual WF fixed point at {theta} = 0 there must exist a novel fixed point at {theta} = {infinity} corresponding to the quartic hermitian matrix model.
Closed string cohomology in open string field theory
NASA Astrophysics Data System (ADS)
Moeller, Nicolas; Sachs, Ivo
2011-07-01
We show that closed string states in bosonic string field theory are encoded in the cyclic cohomology of cubic open string field theory (OSFT) which, in turn, classifies the deformations of OSFT. This cohomology is then shown to be independent of the open string background. Exact elements correspond to closed string gauge transformations, generic boundary deformations of Witten's 3-vertex and infinitesimal shifts of the open string background. Finally it is argued that the closed string cohomology and the cyclic cohomology of OSFT are isomorphic to each other.
Canonical formulation and conserved charges of double field theory
NASA Astrophysics Data System (ADS)
Naseer, Usman
2015-10-01
We provide the canonical formulation of double field theory. It is shown that this dynamics is subject to primary and secondary constraints. The Poisson bracket algebra of secondary constraints is shown to close on-shell according to the C-bracket. A systematic way of writing boundary integrals in doubled geometry is given. By including appropriate boundary terms in the double field theory Hamiltonian, expressions for conserved energy and momentum of an asymptotically flat doubled space-time are obtained and applied to a number of solutions.
Lattice gas models derived from effective field theory
Hamilton, Matthew; Lynch, Iyam; Lee, Dean
2005-04-01
We start from a low-energy effective field theory for interacting fermions on the lattice and expand in the hopping parameter to derive the nearest-neighbor interactions for a lattice gas model. In this model, the renormalization of couplings for different lattice spacings is inherited from the effective field theory, systematic errors can be estimated a priori, and the breakdown of the lattice gas model description at low temperatures can be understood quantitatively. We apply the lattice gas method to neutron matter and compare with results from a recent quantum simulation.
Fluid analog model for boundary effects in field theory
Ford, L. H.; Svaiter, N. F.
2009-09-15
Quantum fluctuations in the density of a fluid with a linear phonon dispersion relation are studied. In particular, we treat the changes in these fluctuations due to nonclassical states of phonons and to the presence of boundaries. These effects are analogous to similar effects in relativistic quantum field theory, and we argue that the case of the fluid is a useful analog model for effects in field theory. We further argue that the changes in the mean squared density are, in principle, observable by light scattering experiments.
Unification of General Relativity with Quantum Field Theory
NASA Astrophysics Data System (ADS)
Ni, Jun
2011-11-01
In the frame of quantum field theory, instead of using the action principle, we deduce the Einstein equation from purely the general covariant principle and the homogeneity of spacetime. The Einstein equation is shown to be the gauge equation to guarantee the local symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field theory, only electroweak-strong interactions should be considered with the curved spacetime metric determined by the Einstein equation.
Holographic Dual of a Boundary Conformal Field Theory
Takayanagi, Tadashi
2011-09-02
We propose a holographic dual of a conformal field theory defined on a manifold with boundaries, i.e., boundary conformal field theory (BCFT). Our new holography, which may be called anti-de Sitter BCFT, successfully calculates the boundary entropy or g function in two-dimensional BCFTs and it agrees with the finite part of the holographic entanglement entropy. Moreover, we can naturally derive a holographic g theorem. We also analyze the holographic dual of an interval at finite temperature and show that there is a first order phase transition.
Toward an axiomatic formulation of noncommutative quantum field theory
Chaichian, M.; Tureanu, A.; Mnatsakanova, M. N.; Nishijima, K.; Vernov, Yu. S.
2011-03-15
We propose new Wightman functions as vacuum expectation values of products of field operators in the noncommutative space-time. These Wightman functions involve the *-product among the fields, compatible with the twisted Poincare symmetry of the noncommutative quantum field theory (NC QFT). In the case of only space-space noncommutativity ({theta}{sub 0i}= 0), we prove the CPT theorem using the noncommutative form of the Wightman functions. We also show that the spin-statistics theorem, demonstrated for the simplest case of a scalar field, holds in NC QFT within this formalism.
A field theory of piezoelectric media containing dislocations
Taupin, V. Fressengeas, C.; Ventura, P.; Lebyodkin, M.
2014-04-14
A field theory is proposed to extend the standard piezoelectric framework for linear elastic solids by accounting for the presence and motion of dislocation fields and assessing their impact on the piezoelectric properties. The proposed theory describes the incompatible lattice distortion and residual piezoelectric polarization fields induced by dislocation ensembles, as well as the dynamic evolution of these fields through dislocation motion driven by coupled electro-mechanical loading. It is suggested that (i) dislocation mobility may be enhanced or inhibited by the electric field, depending on the polarity of the latter, (ii) plasticity mediated by dislocation motion allows capturing long-term time-dependent properties of piezoelectric polarization. Due to the continuity of the proposed electro-mechanical framework, the stress/strain and polarization fields are smooth even in the dislocation core regions. The theory is applied to gallium nitride layers for validation. The piezoelectric polarization fields associated with bulk screw/edge dislocations are retrieved and surface potential modulations are predicted. The results are extended to dislocation loops.
IMPOSING A LAGRANGIAN PARTICLE FRAMEWORK ON AN EULERIAN HYDRODYNAMICS INFRASTRUCTURE IN FLASH
Dubey, A.; Daley, C.; Weide, K.; Graziani, C.; ZuHone, J.
2012-08-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid-structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash
NASA Technical Reports Server (NTRS)
Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.
2012-01-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
Topological BF field theory description of topological insulators
Cho, Gil Young; Moore, Joel E.
2011-06-15
Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
Chern-Simons topological Lagrangians in odd dimensions and their Kaluza-Klein reduction
Wu, Y.
1984-08-01
Clarifying the behavior of generic Chern-Simons secondary invariants under infinitesimal variation and finite gauge transformation, it is proved that they are eligible to be a candidate term in the Lagrangian in odd dimensions (2k-1 for gauge theories and 4k-1 for gravity). The coefficients in front of these terms may be quantized because of topological reasons. As a possible application, the dimensional reduction of such actions in Kaluza-Klein theory is discussed. The difficulty in defining the Chern-Simons action for topologically nontrivial field configurations is pointed out and resolved.
Quantum Energy Inequalities and Stability Conditions in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Fewster, Christopher J.
Quantum Energy Inequalities (QEIs) are constraints on the extent to which quantum fields can violate the energy conditions of classical general relativity. As such they are closely related to the gravitational stability of quantised matter. In this contribution we discuss links between QEIs and other stability conditions in quantum field theory: the microlocal spectrum condition, passivity and nuclearity. The fist two links suggest an interconnection between stability conditions at three different length scales, while the third hints at a deeper origin of QEIs.
Field theory of propagating reaction-diffusion fronts
Escudero, C.
2004-10-01
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean-field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at results already confirmed by numerical simulations.
Aspects of Supersymmetric Field Theories and Complex Geometry
NASA Astrophysics Data System (ADS)
Crichigno, Patricio Marcos
In this dissertation we study various aspects of Supersymmetric Quantum Field Theory and Complex Geometry. We focus on three main aspects. The first is general N = (2, 2) gauged linear sigma models involving semichiral fields. We show that integrating out the semichiral vector multiplet leads to the generalized potential for a hyperkahler manifold, providing a formulation of the hyperkahler quotient in a generalized setting. We then discuss a new quotient construction which leads to non-Kahler manifolds. The second problem we study is motivated by recent developments in the study of the Coulomb branch of supersymmetric theories with a hyperkahler moduli space. A crucial element in these developments is the expression for Darboux coordinates in the hyperkahler manifold. We give a simple derivation of this expression by using projective superspace techniques and we apply this to the study of the moduli space of theories with eight supercharges on R3 x S¹ and R3 x T². Finally, we study the partition function of three-dimensional Chern-Simons theories on S³ with affine ADE quivers. We give a general formula for the partition function of affine D-type quivers in terms of the Chern-Simons levels, providing a prediction for the volume of an infinite family of tri-Sasaki Einstein manifolds corresponding to the gravitational duals of such field theories.
The Effective Field Theory Approach to Fluid Dynamics
NASA Astrophysics Data System (ADS)
Endlich, Solomon George Shamsuddin Osman
In this thesis we initiate a systematic study of fluid dynamics using the effective field theory (EFT) program. We consider the canonical quantization of an ordinary fluid in an attempt to discover if there is some kind of quantum mechanical inconsistency with ordinary fluids at zero temperature. The system exhibits a number of peculiarities associated with the vortex degrees of freedom. We also study the dynamics of a nearly incompressible fluid via (classical) effective field theory. In the kinematical regime corresponding to near incompressibility (small fluid velocities and accelerations), compressional modes are, by definition, difficult to excite, and can be dealt with perturbatively. We systematically outline the corresponding perturbative expansion, which can be thought of as an expansion in the ratio of fluid velocity and speed of sound. This perturbation theory allows us to compute many interesting quantities associated with sound-flow interactions. Additionally, we also improve on the so-called vortex filament model, by providing a local field theory describing the dynamics of vortex-line systems and their interaction with sound, to all orders in perturbation theory. Next, we develop a cosmological model where primordial inflation is driven by a 'solid'. The low energy EFT describing such a system is just a less symmetric version of the action of a fluid---it lacks the volume preserving diffeomorphism. The symmetry breaking pattern of this system differs drastically from that of standard inflationary models: time translations are unbroken. This prevents our model from fitting into the standard effective field theory description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations. And finally, we introduce dissipative effects in the effective field theory of hydrodynamics. We do this in a model-independent fashion by coupling the long-distance degrees of freedom explicitly kept in the effective field theory to a generic sector that "lives in the fluid'', which corresponds physically to the microscopic constituents of the fluid. At linear order in perturbations, the symmetries, the derivative expansion, and the assumption that this microscopic sector is thermalized, allow us to characterize the leading dissipative effects at low frequencies via three parameters only, which correspond to bulk viscosity, shear viscosity, and---in the presence of a conserved charge---heat conduction. Using our methods we re-derive the Kubo relations for these transport coefficients.
Nonlocal scalar quantum field theory from causal sets
NASA Astrophysics Data System (ADS)
Belenchia, Alessio; Benincasa, Dionigi M. T.; Liberati, Stefano
2015-03-01
We study a non-local scalar quantum field theory in flat spacetime derived from the dynamics of a scalar field on a causal set. We show that this non-local QFT contains a continuum of massive modes in any dimension. In 2 dimensions the Hamiltonian is positive definite and therefore the quantum theory is well-defined. In 4-dimensions, we show that the unstable modes of the non-local d'Alembertian are propagated via the so called Wheeler propagator and hence do not appear in the asymptotic states. In the free case studied here the continuum of massive mode are shown to not propagate in the asymptotic states. However the Hamiltonian is not positive definite, therefore potential issues with the quantum theory remain. Finally, we conclude with hints toward what kind of phenomenology one might expect from such non-local QFTs.
Geometric and Topological Methods for Quantum Field Theory
NASA Astrophysics Data System (ADS)
Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.
2013-05-01
Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.
Theory of a ring laser. [electromagnetic field and wave equations
NASA Technical Reports Server (NTRS)
Menegozzi, L. N.; Lamb, W. E., Jr.
1973-01-01
Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.
Sketch of J. R. Kantor's Psychological Interbehavioral Field Theory
ERIC Educational Resources Information Center
Delprato, Dennis J.; Smith, Noel W.
2009-01-01
We provide a sketch of J. R. Kantor's (1959, 1971) psychological interbehavioral field (IBF) theory by identifying 9 essential points and briefly discussing each. The main emphasis of this sketch is on the foundation of Kantor's thinking, the IBF. Suggestions for further study are provided.
Recent Progress in Nuclear Lattice Simulations with Effective Field Theory
NASA Astrophysics Data System (ADS)
Lee, D.
2007-10-01
This proceedings article summarizes recent work presented at Chiral Dynamics 2006 on nuclear lattice simulations with chiral effective field theory for light nuclei. This work has been done in collaboration with Bubar {gra} Borasoy , Evgeny Epelbaum, Hermann Krebs, and Ulf-G. Meißner.
Schr"odinger's Unified Field Theory: Physics by Public Relations
NASA Astrophysics Data System (ADS)
Halpern, Paul
2009-05-01
We will explore the circumstances surrounding Erwin Schr"odinger's announcement in January 1947 that he had developed a comprehensive unified field theory of gravitation and electromagnetism. We will speculate on Schr"odinger's motivations for the mode and tone of his statements, consider the reaction of the international press within the context of the postwar era, and examine Einstein's response.
Field theory of self-organized fractal etching.
Gabrielli, A; Muñoz, M A; Sapoval, B
2001-07-01
We propose a phenomenological field theoretical approach to the chemical etching of a disordered solid. The theory is based on a recently proposed dynamical etching model. Through the introduction of a set of Langevin equations for the model evolution, we are able to map the problem into a field theory related to isotropic percolation. To the best of the author's knowledge, this constitutes the first application of field theory to a problem of chemical dynamics. By using this mapping, many of the etching process critical properties are seen to be describable in terms of the percolation renormalization group fixed point. The emerging field theory has the peculiarity of being self-organized in the sense that without any parameter fine tuning the system develops fractal properties up to a certain scale controlled solely by the volume V of the etching solution. In the limit V-->infinity the upper cutoff goes to infinity and the system becomes scale invariant. We present also a finite size scaling analysis and discuss the relation of this particular etching mechanism to gradient percolation. Finally, the possibility of considering this mechanism as a generic path to self-organized criticality is analyzed, with the characteristics of being closely related to a real physical system and therefore more directly accessible to experiments. PMID:11461332
Avenues of cognition of nongravitational local gauge field theories
NASA Astrophysics Data System (ADS)
Minkowski, Peter
2015-05-01
This controbution is devoted to present basic fearures of a unifying local gauge field theory, prevailing up to a mass scale of approximately 10 16 GeV , allowing the neglect of gravitational curvature effects - indicated by the attribute : 'nongravitational' in the title above.
Unitarization and causalization of nonlocal quantum field theories by classicalization
NASA Astrophysics Data System (ADS)
Addazi, Andrea
2016-01-01
We suggest that classicalization can cure nonlocal quantum field theories from acausal divergences in scattering amplitudes, restoring unitarity and causality. In particular, in “trans-nonlocal” limit, the formation of nonperturbative classical configurations, called classicalons, in scatterings like ϕϕ → ϕϕ, can avoid typical acausal divergences.
Morse theory for vector fields and the Witten Laplacian
Enciso, Alberto; Peralta-Salas, Daniel
2009-05-06
In this paper we informally review some recent developments on the analytical approach to Morse-type inequalities for vector fields. Throughout this work we focus on the main ideas of this approach and emphasize the application of the theory to concrete examples.
An alternative topological field theory of generalized complex geometry
NASA Astrophysics Data System (ADS)
Ikeda, Noriaki; Tokunaga, Tatsuya
2007-09-01
We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is A model in the case that the generalized complex structure depends on only a symplectic structure. Our new model is B model in the case that the generalized complex structure depends on only a complex structure.
Field-Based Concerns about Fourth-Generation Evaluation Theory.
ERIC Educational Resources Information Center
Lai, Morris K.
Some aspects of fourth generation evaluation procedures that have been advocated by E. G. Guba and Y. S. Lincoln were examined empirically, with emphasis on areas where there have been discrepancies between theory and field-based experience. In fourth generation evaluation, the product of an evaluation is not a set of conclusions, recommendations,…
The anomaly and reggeon field theory in QCD
White, A. R.
2000-09-14
The appearance of the U(1) anomaly in the interactions of reggeized gluons is described. Also discussed is the crucial role the anomaly can play in providing the non-perturbative properties necessary for a transition from gluon and quark reggeon diagrams to hadron reggeons and a reggeon field theory description of the pomeron.
Field theory as a tool to constrain new physics models
NASA Astrophysics Data System (ADS)
Maas, Axel
2015-08-01
One of the major problems in developing new physics scenarios is that very often the parameters can be adjusted such that in perturbation theory almost all experimental low-energy results can be accommodated. It is therefore desirable to have additional constraints. Field-theoretical considerations can provide such additional constraints on the low-lying spectrum and multiplicities of models. Especially for theories with elementary or composite Higgs particle the Fröhlich-Morchio-Strocchi (FMS) mechanism provides a route to create additional conditions, though showing it to be at work requires genuine non-perturbative calculations. The qualitative features of this procedure are discussed for generic 2-Higgs-doublet models (2HDMs), grand-unified theories (GUTs) and technicolor-type theories.
Challenges in Lagrangian transport and predictability in 3D flows
NASA Astrophysics Data System (ADS)
Branicki, M.; Wiggins, S.; Kirwan, A. D.; Malek-Madani, R.
2011-12-01
The interplay between the geometrical theory of dynamical systems and the trajectory-based description of aperiodically time-dependent fluid flows has led to significant advances in understanding the role of chaotic transport in geophysical flows at scales dominated by advection. Lagrangian transport analysis utilizing either the time-dependent geometry of intersecting stable and unstable manifolds of the so-called Distinguished Hyperbolic Trajectories (DHT), or ridges of finite-time Lyapunov exponent fields (LCS), provide a much needed and complementary insight into ephemeral mechanisms responsible for the existence of `leaky' transport barriers and 'leaky' mesoscale eddies. However, to date most oceanic applications have been confined to 2D analysis of near surface regions in 'perfect' flows not accounting for model or measurement error, and with the tacit assumption of negligible vertical velocities. I will systematically address issues concerning the regimes of applicability of two-dimensional analysis in 3D aperiodically time-dependent flows, as well as outstanding challenges in fully 3D Lagrangian transport analysis. Even for perfect horizontal velocities, little is known about the vertical extent of stable/unstable manifolds associated with DHTs and/or other special structures relevant to stratified 3D flows. In particular, their sensitivity to errors in the vertical velocities and data assimilation methods has been little studied. Rigorous results regarding the above issues will be illustrated by revealing and mathematically tractable toy models, as well as examples from a detailed study in an eddy-rich region from the Gulf of Mexico and the Mediterranean. New ways of quantifying the uncertainty in Lagrangian predictions will also be presented.
Numerical Studies of Fermionic Field Theories at - N
NASA Astrophysics Data System (ADS)
Dickens, Thomas Allen
1987-09-01
Several fermionic quantum field theories are studied in the Large- N limit by using a numerical algorithm which exploits the classical nature of this limit. The classical limit is studied as a variational problem on a space of coherent states constructed from the quantum operators of the theory. Various quantities, such as the expectation values of observables, the ground state energy, and the mass spectrum, may be easily obtained. A description of the algorithm, which may be used to study large- N theories with or without fermions, is presented. As an initial test of the method, the spectrum of continuum QCD in 1 + 1 dimensions is determined and compared to previously obtained results. Exact solutions of 1 + 1 dimensional lattice versions of the free fermion theory, the Gross -Neveu model, and QCD are obtained. Comparison of these exact results with results from the numerical algorithm is used to test the algorithms, and more importantly, to determine the errors incurred from the approximations used in the numerical technique. Numerical studies of the above three lattice theories in higher dimensions are also presented. The results are again compared to exact solutions for free fermions and the Gross-Neveu model; perturbation theory is used to derive expansions with which the numerical results for QCD may be compared. The numerical algorithm may also be used to study the euclidean formulation of lattice gauge theories. Results for 1 + 1 dimensional euclidean lattice QCD are compared to the exact solution of this model.
Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory
ERIC Educational Resources Information Center
Tweney, Ryan D.
2011-01-01
James Clerk Maxwell "translated" Michael Faraday's experimentally-based field theory into the mathematical representation now known as "Maxwell's Equations." Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of…
Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory
ERIC Educational Resources Information Center
Tweney, Ryan D.
2011-01-01
James Clerk Maxwell "translated" Michael Faraday's experimentally-based field theory into the mathematical representation now known as "Maxwell's Equations." Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of
Redshift distortions of clustering: a Lagrangian approach.
NASA Astrophysics Data System (ADS)
Hivon, E.; Bouchet, F. R.; Colombi, S.; Juszkiewicz, R.
1995-06-01
We study the effects of peculiar velocities on statistical measures of galaxy clustering. These effects occur when distances to the galaxies are estimated from their redshifts. It is assumed that the clustering pattern results from the gravitational instability of initially Gaussian, small-amplitude perturbations of a Friedman-Lemaitre cosmological model. Explicit expressions are given for an arbitrary density parameter {OMEGA} of the model, both when the cosmological constant, {LAMBDA}, is zero, and when the model is spatially flat, {OMEGA}+ {LAMBDA}/3H^2^ =1. Kaiser (1987) had analyzed the redshift distortion of the two-point correlation function. This function determines the variance of the density field distribution function and can be computed using linear perturbation theory. We show here how to compute higher order moments in redshift space, paying special attention to the skewness, or third moment of the density field, and its Fourier space counterpart, the bispectrum. This calls for a weakly non-linear analysis. We rely on a perturbative expansion of particle trajectories in Lagrangian coordinates, using the formalism introduced by Moutarde et al. (1991) and further developed by Bouchet et al. (1992, 1994). This formalism extends to higher orders the Zel'dovich first order (i.e. linear) solution (1970). The lowest non-vanishing contribution to the skewness comes from the first and second-order terms in perturbation theory. Therefore, using Zel'dovich approximation would not be self-consistent and would yield inaccurate results. We show that a physically consistent and quantitatively accurate analysis of the growth skewness in redshift space can be obtained from second-order Lagrangian theory. With practical applications to redshift surveys in mind, we also study the effects of spatial smoothing of the evolved density field. The necessary formalism was developed by Juszkiewicz & Bouchet (1991) and Juszkiewicz et al. (1993a). Here we give the first complete account of these calculations; we also extend the formalism by explicitly taking redshift distortions into account. We give analytic expressions for the gravitationally induced skewness as a function of the power spectrum and of {OMEGA}, for a spherical top-hat and a Gaussian smoothing filter. We compare our analytical predictions with measurements performed in numerical simulations, and find good agreement. These results should then prove useful in analyzing large scale redshift surveys. In particular, our results, in conjunction with the recent suggestion of Fry (1994), may solve a well known problem which always arises in conventional dynamical determinations of the mean density of the universe. Such studies produce estimates of {OMEGA} which are coupled with the parameters describing the bias in the galaxy distribution. As a result, a biased {OMEGA}= 1 model is dynamically indistinguishable from an open, unbiased, one. For the first time, it may become possible to break this degeneracy, and decouple the estimates of linear and non-linear bias from the estimates of {OMEGA} and {LAMBDA}.
Gauge fields in graphene with nonuniform elastic deformations: A quantum field theory approach
NASA Astrophysics Data System (ADS)
Arias, Enrique; Hernández, Alexis R.; Lewenkopf, Caio
2015-12-01
We investigate the low-energy continuum limit theory for electrons in a graphene sheet under strain. We use the quantum field theory in curved spaces to analyze the effect of the system deformations into an effective gauge field. We study both in-plane and out-of-plane deformations and obtain a closed expression for the effective gauge field due to arbitrary nonuniform sheet deformations. The obtained results reveal a remarkable relation between the local-pseudomagnetic field and the Riemann curvature, so far overlooked.
M Theory on AdSp x 511-p and superconformal field theories
Aharony, Ofer; Yaron, Oz; Zheng, Yin
1998-04-01
We study the large N limit of the interacting superconformal field theories associated with N M5 branes or M2 branes using the recently proposed relation between these theories and M theory on AdS spaces. We first analyze the spectrum of chiral operators of the 6d (0, 2) theory associated with M5 branes in flat space, and find full agreement with earlier results obtained using its DLCQ description as quantum mechanics on a moduli space of instantons. We then perform a similar analysis for the D{sub N} type 6d (0, 2) theories associated with M5 branes at an R{sup 5}/Z{sub 2} singularity, and for the 3d N = 8 superconformal field theories associated with M2 branes in flat space and at an R{sup 8}/Z{sub 2} singularity respectively. Little is known about these three theories, and our study yields for the first time their spectrum of chiral operators (in the large N limit).
Effective field theory in larger clusters - Ising model
NASA Astrophysics Data System (ADS)
Akıncı, Ümit
2015-07-01
General formulation for the effective field theory with differential operator technique and the decoupling approximation with larger finite clusters (namely EFT-N formulation) has been derived for several S-1/2 bulk systems. The effect of enlarging this finite cluster on the results for the critical temperatures and thermodynamic properties has been investigated in detail. Beside the improvement on the critical temperatures, the necessity of using larger clusters, especially in nanomaterials has been discussed. Using the derived formulation, applications on the effective field and mean field renormalization group techniques have also been performed.
New symbolic tools for differential geometry, gravitation, and field theory
NASA Astrophysics Data System (ADS)
Anderson, I. M.; Torre, C. G.
2012-01-01
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein equations, and symmetry reduction of field equations.
Massive basketball diagram for a thermal scalar field theory
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-15
The ''basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a {phi}{sup 4} interaction to three-loop order. (c) 2000 The American Physical Society.
Reconstructing inflationary paradigm within Effective Field Theory framework
NASA Astrophysics Data System (ADS)
Choudhury, Sayantan
2016-03-01
In this paper my prime objective is to analyse the constraints on a sub-Planckian excursion of a single inflaton field within Effective Field Theory framework in a model independent fashion. For a generic single field inflationary potential, using the various parameterization of the primordial power spectrum I have derived the most general expression for the field excursion in terms of various inflationary observables, applying the observational constraints obtained from recent Planck 2015 and Planck 2015 + BICEP2/Keck Array data. By explicit computation I have reconstructed the structural form of the inflationary potential by constraining the Taylor expansion co-efficients appearing in the generic expansion of the potential within the Effective Field Theory. Next I have explicitly derived, a set of higher order inflationary consistency relationships, which would help us to break the degeneracy between various class of inflationary models by differentiating them. I also provided two simple examples of Effective Theory of inflation- inflection-point model and saddle-point model to check the compatibility of the prescribed methodology in the light of Planck 2015 and Planck 2015 + BICEP2/Keck Array data. Finally, I have also checked the validity of the prescription by estimating the cosmological parameters and fitting the theoretical CMB TT, TE and EE angular power spectra with the observed data within the multipole range 2 < l < 2500.
Laser theory with finite atom-field interacting time
NASA Astrophysics Data System (ADS)
Yu, Deshui; Chen, Jingbiao
2008-07-01
We investigate the influence of atomic transit time τ on the laser linewidth by the quantum Langevin approach. With comparing the bandwidths of cavity mode κ , atomic polarization γab , and atomic transit broadening τ-1 , we study the laser linewidth in different limits. We also discuss the spectrum of fluctuations of output field and the influence of pumping statistics on the output field.The influence of atomic transit time τ on laser field has not been carefully discussed before, to our knowledge. In particular, a laser operating in the region of γab≪τ-1≪κ/2 appears not to have been analyzed in previous laser theories. Our work could be a useful complementarity to laser theory. It is also an important theoretical foundation for the recently proposed active optical atomic clock based on bad-cavity laser mechanism.
Space-Time Resolved Approach for Interacting Quantum Field Theories
Wagner, R. E.; Ware, M. R.; Shields, B. T.; Su, Q.; Grobe, R.
2011-01-14
An alternative approach to the usual perturbative S-matrix evaluation of quantum field theories is presented which is nonperturbative and provides full space-time resolution. We study the dynamical development of the force between two fermion wave packets for the Yukawa system. The spatial distribution of the virtual bosons that act as mediators of the force can be analyzed along with the fermionic densities. Using a potential function for the fermion-fermion interaction is a good approximation to the field theoretical calculations when the Fock space is restricted to only one boson, but in the full quantum field theory the fermion-fermion force is enhanced by higher-order multiboson processes. Furthermore, the normally attractive fermion-fermion Yukawa force can, in principle, be manipulated to even be repulsive if the momentum modes available to the virtual bosons are restricted.
Entanglement spectrum in cluster dynamical mean-field theory
NASA Astrophysics Data System (ADS)
Udagawa, Masafumi; Motome, Yukitoshi
2015-01-01
We study the entanglement spectrum of the Hubbard model at half filling on a kagome lattice. The entanglement spectrum is defined by the set of eigenvalues of a reduced thermal density matrix, which is naturally obtained in the framework of the dynamical mean-field theory. Adopting the cluster dynamical mean-field theory combined with continuous-time auxiliary-field Monte Carlo method, we calculate the entanglement spectrum for a three-site triangular cluster in the kagome Hubbard model. We find that the results at the three-particle sector well capture the qualitative nature of the system. In particular, the eigenvalue of the reduced density matrix, corresponding to the chiral degrees of freedom, exhibits a characteristic temperature scale Tchiral, below which a metallic state with large quasiparticle mass is stabilized. The entanglement spectra at different particle number sectors also exhibit characteristic changes around Tchiral, implying the development of inter-triangular ferromagnetic correlations in the correlated metallic regime.
Topologically stratified energy minimizers in a product Abelian field theory
NASA Astrophysics Data System (ADS)
Han, Xiaosen; Yang, Yisong
2015-09-01
We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from Ns vortices and Ps anti-vortices (s = 1, 2) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface S which states that a solution with prescribed N1, N2 vortices and P1, P2 anti-vortices of two designated species exists if and only if the inequalities
PERTURBATION THEORY OF THE COSMOLOGICAL LOG-DENSITY FIELD
Wang Xin; Chen Xuelei; Neyrinck, Mark; Szalay, Alex; Szapudi, Istvan; Lesgourgues, Julien; Riotto, Antonio; Sloth, Martin
2011-07-01
The matter density field exhibits a nearly lognormal probability density distribution after entering into the nonlinear regime. Recently, it has been shown that the shape of the power spectrum of a logarithmically transformed density field is very close to the linear density power spectrum, motivating an analytic study of it. In this paper, we develop cosmological perturbation theory for the power spectrum of this field. Our formalism is developed in the context of renormalized perturbation theory, which helps to regulate the convergence behavior of the perturbation series, and of the Taylor series expansion we use for the logarithmic mapping. This approach allows us to handle the critical issue of density smoothing in a straightforward way. We also compare our perturbative results with simulation measurements.
Entanglement of Low-Energy Excitations in Conformal Field Theory
Alcaraz, Francisco Castilho; Ibanez Berganza, Miguel; Sierra, German
2011-05-20
In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Renyi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the nth Renyi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT.
Quantum field theory for condensation of bosons and fermions
De Souza, Adriano N.; Filho, Victo S.
2013-03-25
In this brief review, we describe the formalism of the quantum field theory for the analysis of the condensation phenomenon in bosonic systems, by considering the cases widely verified in laboratory of trapped gases as condensate states, either with attractive or with repulsive two-body interactions. We review the mathematical formulation of the quantum field theory for many particles in the mean-field approximation, by adopting contact interaction potential. We also describe the phenomenon of condensation in the case of fermions or the degenerate Fermi gas, also verified in laboratory in the crossover BEC-BCS limit. We explain that such a phenomenon, equivalent to the bosonic condensation, can only occur if we consider the coupling of particles in pairs behaving like bosons, as occurs in the case of Cooper's pairs in superconductivity.
Theory of Interacting Bloch Electrons in a Magnetic Field
NASA Astrophysics Data System (ADS)
Kita, Takafumi; Arai, Masao
2005-10-01
We study interacting electrons in a periodic potential and a uniform magnetic field B taking the spin-orbit interaction into account. We first establish a perturbation expansion for those electrons with respect to the Bloch states in zero field. It is shown that the expansion can be performed with the zero-field Feynman diagrams of satisfying the momentum and energy conservation laws. We thereby clarify the structures of the self-energy and the thermodynamic potential in a finite magnetic field. We also provide a prescription of calculating the electronic structure in a finite magnetic field within the density functional theory starting from the zero-field energy-band structure. On the basis of these formulations, we derive explicit expressions for the magnetic susceptibility of B → 0 at various approximation levels on the interaction, particularly within the density functional theory, which include the result of Roth [J. Phys. Chem. Solids \\textbf{23} (1962) 433] as the non-interacting limit. We finally study the de Haas--van Alphen oscillation in metals to show that quasiparticles at the Fermi level with the many-body effective mass are directly relevant to the phenomenon. The present argument may be more transparent than that by Luttinger [Phys. Rev. \\textbf{121} (1961) 1251] of using the gauge invariance and has an advantage that the change of the band structure with the field may be incorporated.
Functional integral for non-Lagrangian systems
Kochan, Denis
2010-02-15
A functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The approach, which we call ''stringy quantization,'' is based solely on classical equations of motion and is free of any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force -{kappa}q{sup A}. Results for A=1 are compared with those obtained in the approaches by Caldirola-Kanai, Bateman, and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.
Kinetic Ising model in a time-dependent oscillating external magnetic field: effective-field theory
NASA Astrophysics Data System (ADS)
Bayram, Deviren; Osman, Canko; Mustafa, Keskin
2010-05-01
Recently, Shi et al. [2008 Phys. Lett. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tom and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tom and de Oliveira; hence the dynamic phase diagrams calculated by Shi et al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (?) and static external field amplitude (h0) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of ? and h0.
The unitary conformal field theory behind 2D Asymptotic Safety
NASA Astrophysics Data System (ADS)
Nink, Andreas; Reuter, Martin
2016-02-01
Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in d > 2 dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge c = 25. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a complete quenching of the a priori expected Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this prediction to Monte Carlo results obtained in the discrete approach to 2D quantum gravity based upon causal dynamical triangulations is mentioned. Similarities of the fixed point theory to, and differences from, non-critical string theory are also described. On the technical side, we provide a detailed analysis of an intriguing connection between the Einstein-Hilbert action in d > 2 dimensions and Polyakov's induced gravity action in two dimensions.
The Effective Field Theory of Dark Matter and Structure Formation
NASA Astrophysics Data System (ADS)
Hertzberg, Mark P
2014-06-01
We develop the effective field theory of cosmological large scale structure. We start from the collisionless Boltzmann equation and integrate out short modes of a dark matter/dark energy dominated universe (LambdaCDM) whose matter is comprised of massive particles as used in cosmological simulations. This establishes a long distance effective fluid, valid for length scales larger than the non-linear scale ~ 10 Mpc, and provides the complete description of large scale structure formation. Extracting the time dependence, we derive recursion relations that encode the perturbative solution. This is exact for the matter dominated era and quite accurate in LambdaCDM also. The effective fluid is characterized by physical parameters, including sound speed and viscosity. These two fluid parameters play a degenerate role with each other and lead to a relative correction from standard perturbation theory of the form ~ 10^{-6}c^2k^2/H^2. Starting from the linear theory, we calculate corrections to cosmological observables, such as the baryon-acoustic-oscillation peak, which we compute semi-analytically at one-loop order. Due to the non-zero fluid parameters, the predictions of the effective field theory agree with observation much more accurately than standard perturbation theory and we explain why. We also discuss corrections from treating dark matter as interacting or wave-like and other issues.
Kriz, Igor; Loebl, Martin; Somberg, Petr
2013-05-15
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding conjectured limits realized by fermions in rational conformal field theories.
Topics in field theory-higher spins, CFT, and gravity
Yang, Z.
1990-01-01
Several topics in field theory are investigated. (1) Massive higher spin actions are obtained as gauge theories from the dimensional reduction of the corresponding massless ones. (2) The author considers a model of spin4 and spin2 interaction through the Bel-Robinson tensor of spin2 field, which in conserved at free level. The coupling is inconsistent, yet there are indications that adding still higher spin couplings would be a promising direction to achieve consistency. (3) Energy and Stability of Einstein-Gauss-Bonnet models of gravity are studied. It is shown that flat space is stable while AdS is not. (4) Gauged Wess-Zumino-Witten models are studied in detail. The equivalence to GKO construction of conformal field theory is considered. BRST quantization of the models is given. (5) Nonrenormalizability of quantum gravity is, in the binomial first order metric formulation, traced to a mismatch between the symmetries of its quadratic and cubic term. (6) The possibility that the gravitational model defined in D = 3 by an action which is the sum of Einstein and Chern-Simons terms is a viable quantum theory is investigated. It is shown that it is compatible with power-counting renormalizability. Gauge invariant regularizations, however, have not been found to exist. Detailed BRS analysis shows that there are possible anomalies.
Lie algebraic structures in integrable models, affine Toda field theory
NASA Astrophysics Data System (ADS)
Korff, Christian
2000-08-01
The most prominent class of integrable quantum field theories in 1+1 dimensions is affine Toda theory. Distinguished by a rich underlying Lie algebraic structure these models have in recent years attracted much attention not only as test laboratories for non-perturbative methods in quantum field theory but also in the context of off-critical models. After a short introduction the mathematical preliminaries such as root systems, Coxeter geometry, dual algebras, q-deformed Coxeter elements and q-deformed Cartan matrices are introduced. Using this mathematical framework the bootstrap analysis of the affine Toda S-matrices with real coupling is performed and several universal Lie algebraic formulae proved. The Lie algebraic methods are then extended to define a new class of colour valued S-matrices and also here universal expressions are derived. The second part of the thesis presents a detailed analysis of the high-energy regime of the integrable models discussed in the first part. By means of the thermodynamic Bethe ansatz the central charges of the ultraviolet conformal field theories are calculated and in case of affine Toda theories also the first order term in the scaling function is analytically obtained. For the colour valued S-matrices the connection to WZNW coset models is discussed. A particular subclass of them, the so-called Homogeneous Sine-Gordon models, is investigated in some detail and it is found that the presence of unstable particles in these theories gives rise to a staircase pattern in the corresponding scaling function. This thesis summarizes the results of previously published articles listed in the introduction.
Lagrangian analysis of hemodynamics data from FSI simulation
Duvernois, Vincent; Marsden, Alison L.; Shadden, Shawn C.
2013-01-01
We present the computation of Lagrangian-based flow characterization measures for time-dependent, deformable-wall, finite-element blood flow simulations. Applicability of the algorithm is demonstrated in a fluid–structure interaction simulation of blood flow through a total cavopulmonary connection (Fontan procedure), and results are compared with a rigid-vessel simulation. Specifically, we report on several important Lagrangian-based measures including flow distributions, finite-time Lyapunov exponent fields, particle residence time, and exposure time calculations. Overall, strong similarity in Lagrangian measures of the flow between deformable and rigid-vessel models was observed. PMID:23559551
Alternative refined Gribov-Zwanziger Lagrangian
Gracey, J. A.
2010-10-15
We consider the implications of the condensation of a general local Becchi-Rouet-Stora-Tyutin invariant dimension two operator built out of the localizing ghost fields of the Gribov-Zwanziger Lagrangian which is a localized Lagrangian incorporating the Gribov problem in the Landau gauge. For different color tensor projections of the general operator, the properties of a frozen gluon propagator and unenhanced Faddeev-Popov ghost propagator, which are observed in lattice computations, can be reproduced. The alternative possibilities are distinguished by the infrared structure of the propagators of the spin-1 fields, other than those of the gluon and Faddeev-Popov ghost, for which there is no numerical simulation data to compare with yet.
Axiomatics of Galileo-invariant quantum field theory
Dadashev, L.A.
1986-03-01
The aim of this paper is to construct the axiomatics of Galileo-invariant quantum field theory. The importance of this problem is demonstrated from various points of view: general properties that the fields and observables must satisfy are considered; S-matrix nontriviality of one such model is proved; and the differences from the relativistic case are discussed. The proposed system of axioms is in many respects analogous to Wightman axiomatics, but is less general. The main result is contained in theorems which describe the admissible set of initial fields and total Hamiltonians, i.e., precisely the two entities that completely determine interacting fields. The author considers fields that prove the independence of some axioms.
Double metric, generalized metric, and α' -deformed double field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Zwiebach, Barton
2016-03-01
We relate the unconstrained "double metric" of the "α' -geometry" formulation of double field theory to the constrained generalized metric encoding the spacetime metric and b -field. This is achieved by integrating out auxiliary field components of the double metric in an iterative procedure that induces an infinite number of higher-derivative corrections. As an application, we prove that, to first order in α' and to all orders in fields, the deformed gauge transformations are Green-Schwarz-deformed diffeomorphisms. We also prove that to first order in α' the spacetime action encodes precisely the Green-Schwarz deformation with Chern-Simons forms based on the torsionless gravitational connection. This seems to be in tension with suggestions in the literature that T-duality requires a torsionful connection, but we explain that these assertions are ambiguous since actions that use different connections are related by field redefinitions.
Nuclear axial currents in chiral effective field theory
Baroni, Alessandro; Girlanda, Luca; Pastore, Saori; Schiavilla, Rocco; Viviani, Michele
2016-01-11
Two-nucleon axial charge and current operators are derived in chiral effective field theory up to one loop. The derivation is based on time-ordered perturbation theory and accounts for cancellations between the contributions of irreducible diagrams and the contributions owing to nonstatic corrections from energy denominators of reducible diagrams. Ultraviolet divergencies associated with the loop corrections are isolated in dimensional regularization. The resulting axial current is finite and conserved in the chiral limit, while the axial charge requires renormalization. As a result, a complete set of contact terms for the axial charge up to the relevant order in the power countingmore » is constructed.« less
Advanced mean-field theory of the restricted Boltzmann machine.
Huang, Haiping; Toyoizumi, Taro
2015-05-01
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean-field theory based on the Bethe approximation. Our theory provides an efficient message-passing-based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those obtained by the computationally expensive sampling-based method. PMID:26066098
Nuclear axial currents in chiral effective field theory
NASA Astrophysics Data System (ADS)
Baroni, A.; Girlanda, L.; Pastore, S.; Schiavilla, R.; Viviani, M.
2016-01-01
Two-nucleon axial charge and current operators are derived in chiral effective field theory up to one loop. The derivation is based on time-ordered perturbation theory and accounts for cancellations between the contributions of irreducible diagrams and the contributions owing to nonstatic corrections from energy denominators of reducible diagrams. Ultraviolet divergencies associated with the loop corrections are isolated in dimensional regularization. The resulting axial current is finite and conserved in the chiral limit, while the axial charge requires renormalization. A complete set of contact terms for the axial charge up to the relevant order in the power counting is constructed.
Conformal invariance for non-relativistic field theory
NASA Astrophysics Data System (ADS)
Mehen, T.; Stewart, I. W.; Wise, M. B.
2000-02-01
Momentum space Ward identities are derived for the amputated n-point Green's functions in /3+1 dimensional non-relativistic conformal field theory. For /n=4 and /6 the implications for scattering amplitudes (i.e. on-shell amputated Green's functions) are considered. Any scale invariant 2-to-2 scattering amplitude is also conformally invariant. However, conformal invariance imposes constraints on off-shell Green's functions and the three particle scattering amplitude which are not automatically satisfied if they are scale invariant. As an explicit example of a conformally invariant theory we consider non-relativistic particles in the infinite scattering length limit.
Heavy dark matter annihilation from effective field theory.
Ovanesyan, Grigory; Slatyer, Tracy R; Stewart, Iain W
2015-05-29
We formulate an effective field theory description for SU(2)_{L} triplet fermionic dark matter by combining nonrelativistic dark matter with gauge bosons in the soft-collinear effective theory. For a given dark matter mass, the annihilation cross section to line photons is obtained with 5% precision by simultaneously including Sommerfeld enhancement and the resummation of electroweak Sudakov logarithms at next-to-leading logarithmic order. Using these results, we present more accurate and precise predictions for the gamma-ray line signal from annihilation, updating both existing constraints and the reach of future experiments. PMID:26066425
Advanced mean-field theory of the restricted Boltzmann machine
NASA Astrophysics Data System (ADS)
Huang, Haiping; Toyoizumi, Taro
2015-05-01
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean-field theory based on the Bethe approximation. Our theory provides an efficient message-passing-based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those obtained by the computationally expensive sampling-based method.
Stochastic quantization of real-time thermal field theory
Aguiar, T. C. de; Svaiter, N. F.; Menezes, G.
2010-10-15
We use the stochastic quantization method to obtain the free scalar propagator of a finite temperature field theory formulated in the Minkowski space-time. First, we use the Markovian stochastic quantization approach to present the two-point function of the theory. Second, we assume a Langevin equation with a memory kernel and a colored noise. The convergence of the Markovian and non-Markovian stochastic processes in the asymptotic limit of the fictitious time is obtained. Our formalism can be the starting point to discuss systems at finite temperature out of equilibrium.