Symmetries in Lagrangian Field Theory
Lucía Búa; Ioan Bucataru; Manuel de León; Modesto Salgado; Silvia Vilariño
2015-02-03
By generalizing 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 $J^1\\pi$ of a fiber bundle $\\pi:E\\to {\\mathbb R}^k$ where ${\\mathbb R}^k$ is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether Theorem is proved.
A Lagrangian effective field theory
NASA Astrophysics Data System (ADS)
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-01
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory.
Unambiguous formalism for higher order Lagrangian field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David; Vankerschaver, Joris
2009-11-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
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.
A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories
Li, Wenliang
2015-01-01
We develop a general framework for Lorentz-invariant Lagrangian field theories that leads to second order equations of motion. The key ingredient is the antisymmetric Kronecker delta. Then we reformulate the general ghost-free Lagrangians in the language of differential forms. The absence of higher order equations of motion stems from the basic fact that every exact form is closed. All known ghost-free Lagrangian theories for spin-0, spin-1, spin-2 fields have natural formulations in this framework. We propose new ghost-free Lagrangians, for example, novel nonlinear kinetic terms for graviton.
M. M. Sharma
2008-07-03
A new Lagrangian model without nonlinear scalar self-interactions in the relativistic mean-field (RMF) theory is proposed. Introducing terms for scalar-vector interactions (SVI), we have developed a RMF Lagrangian model for finite nuclei and nuclear matter. It is shown that by inclusion of SVI in the basic RMF Lagrangian, the nonlinear sigma^3 and sigma^4 terms can be dispensed with. The SVI Lagrangian thus obtained provides a good description of ground-state properties of nuclei along the stability line as well as far away from it. This Lagrangian model is also able to describe experimental data on the breathing-mode giant monopole resonance energies well.
On the notion of gauge symmetries of generic Lagrangian field theory
Giachetta, G.; Mangiarotti, L. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Sardanashvily, G. [Department of Theoretical Physics, Moscow State University, 117234 Moscow (Russian Federation)
2009-01-15
General Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Its nontrivial reducible gauge symmetries and their algebra are defined in this very general setting by means of the inverse second Noether theorem. In contrast with gauge symmetries, nontrivial Noether and higher-stage Noether identities of Lagrangian theory can be intrinsically defined by constructing the exact Koszul-Tate complex. The inverse second Noether theorem that we prove associates with this complex the cochain sequence with the ascent operator whose components define nontrivial gauge and higher-stage gauge symmetries. These gauge symmetries are said to be algebraically closed if the ascent operator can be extended to a nilpotent operator. The necessary conditions for this extension are stated. The characteristic examples of Yang-Mills supergauge theory, topological Chern-Simons theory, gauge gravitation theory, and topological background field (BF) theory are presented.
A Mathematical Base for Fibre Bundle Formulation of Lagrangian Quantum Field Theory
Iliev, Bozhidar Z. [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee, 1784 Sofia (Bulgaria)
2011-04-07
The paper contains a differential-geometric foundations for an attempt to formulate Lagrangian (canonical) quantum field theory on fibre bundles. In it the standard Hilbert space of quantum field theory is replace with a Hilbert bundle; the former playing a role of a (typical) fibre of the letter one. Suitable sections of that bundle replace the ordinary state vectors and the operators on the system's Hilbert space are transformed into morphisms of the same bundle. In particular, the field operators are mapped into corresponding field morphisms.
A study on relativistic lagrangian field theories with non-topological soliton solutions
Diaz-Alonso, J. [LUTH, Observatoire de Paris, CNRS, Universite Paris Diderot, 5 Place Jules Janssen, 92190 Meudon (France); Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias (Spain)], E-mail: joaquin.diaz@obspm.fr; Rubiera-Garcia, D. [Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias (Spain)
2009-04-15
We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gauge-invariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call 'admissible' models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore, we perform a general spectral analysis of the dynamic evolution of the small perturbations around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finite-energy electrostatic spherically symmetric solutions which, unlike the (multi-) scalar case, are not always stable. The variational analysis of the energy functional leads now to supplementary restrictions to be imposed on the lagrangian densities in order to ensure the linear stability of the solitons. We establish a correspondence between any admissible soliton-supporting (multi-) scalar model and a family of admissible generalized gauge models supporting finite-energy electrostatic point-like solutions. Conversely, for each admissible soliton-supporting gauge-invariant model there is an associated unique admissible (multi-) scalar model with soliton solutions. This shows the exhaustive character of the admissibility and stability conditions in determining the class of soliton-supporting generalized gauge models. The usual Born-Infeld electrodynamic theory and its non-abelian extensions are shown to be (very particular) examples of one of these families.
Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches
NASA Astrophysics Data System (ADS)
Antonowicz, Marek; Szczyrba, Wiktor
1985-06-01
We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.
The Lagrangian-space Effective Field Theory of large scale structures
Porto, Rafael A.; Zaldarriaga, Matias [School of Natural Sciences, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540 (United States); Senatore, Leonardo, E-mail: rporto@ias.edu, E-mail: senatore@stanford.edu, E-mail: matiasz@ias.edu [Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94306 (United States)
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.
Emmanuele Battista; Simone Dell'Agnello; Giampiero Esposito; Luciano Di Fiore; Jules Simo; Aniello Grado
2015-07-10
In the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid, we 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. We then 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. 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. By virtue of the effective-gravity correction to the longdistance form of the potential among two point 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 two millimeters, 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 meters, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 meters per orbit. Thus, it is possible to conceive a new, first-generation laser ranging test of general relativity with a relative accuracy in between 1/100 and 1/1000, by measuring the 7.61-meter correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. This will be the basis to consider a second-generation experiment to set experimental constraints on deviations of effective field theories of gravity from general relativity.
Emmanuele Battista; Simone Dell'Agnello; Giampiero Esposito; Luciano Di Fiore; Jules Simo; Aniello Grado
2015-09-09
In the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid, we 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. We then 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. 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. By virtue of the effective-gravity correction to the longdistance form of the potential among two point 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 two millimeters, 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 meters, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 meters per orbit. Thus, it is possible to conceive a new, first-generation laser ranging test of general relativity with a relative accuracy in between 1/100 and 1/1000, by measuring the 7.61-meter correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. This will be the basis to consider a second-generation experiment to set experimental constraints on deviations of effective field theories of gravity from general relativity.
Grassmann-graded Lagrangian theory of even and odd variables
G. Sardanashvily
2012-06-12
Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems, characterized by hierarchies of non-trivial higher-order Noether identities and gauge symmetries. This is a general case of classical field theory and Lagrangian non-relativistic mechanics.
The recursion relation in Lagrangian perturbation theory
Rampf, Cornelius, E-mail: rampf@physik.rwth-aachen.de [Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen, D-52056 Aachen (Germany)
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.
The n-symplectic Algebra of Observables Covariant Lagrangian Field Theory
Norris, Larry K.
a "modified n-symplectic potential" ^L on LE, the Cartan-Hamilton-Poincar´e (CHP) Rn -valued 1-form, multisymplectic geometry, frame bundle, Hamiltonian field theories, Poisson bracket, jet bundles, contact . If : LE J1 then we put L := (L). Using a lifted Legendre transformation we construct the Cartan-Hamilton
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.
P- and T-Violating Lagrangians in Chiral Effective Field Theory and Nuclear Electric Dipole Moments
J. Bsaisou; Ulf-G. Meißner; A. Nogga; A. Wirzba
2015-04-30
A scheme to derive hadronic interactions induced by effective multi-quark terms is presented within the framework of chiral effective field theory. It is employed to work out the list of parity- and time-reversal-symmetry-violating hadronic interactions that are relevant for the computation of nuclear contributions to the electric dipole moments of the hydrogen-2, helium-3 and hydrogen-3 nuclei. We also derive the scattering and Faddeev equations required to compute electromagnetic form factors in general and electric dipole moments in particular.
Battista, Emmanuele; Esposito, Giampiero; Di Fiore, Luciano; Simo, Jules; Grado, Aniello
2015-01-01
In the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid, we 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. We then 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. 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. By virtue of the effective-gravity correction to the longdistance form of the potential among two point 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 ...
Thermal effective Lagrangian of static gravitational fields
NASA Astrophysics Data System (ADS)
Brandt, F. T.; Siqueira, J. B.
2012-03-01
We compute the effective Lagrangian of static gravitational fields interacting with thermal fields. Our approach employs the usual imaginary time formalism as well as the equivalence between the static and space-time independent external gravitational fields. This allows to obtain a closed form expression for the thermal effective Lagrangian in d space-time dimensions.
Thermal Effective Lagrangian of Static Gravitational Fields
F T Brandt; J B Siqueira
2012-03-08
We compute the effective Lagrangian of static gravitational fields interacting with thermal fields. Our approach employs the usual imaginary time formalism as well as the equivalence between the static and space-time independent external gravitational fields. This allows to obtain a closed form expression for the thermal effective Lagrangian in $d$ space-time dimensions.
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.
Fibre Bundles, Jet Manifolds and Lagrangian Theory. Lectures for Theoreticians
G. Sardanashvily
2009-09-29
In contrast with QFT, classical field theory can be formulated in a strict mathematical way by treating classical fields as sections of smooth fibre bundles. Addressing to the theoreticians, these Lectures aim to compile the relevant material on fibre bundles, jet manifolds, connections, graded manifolds and Lagrangian theory. They follow the perennial course of lectures on geometric methods in field theory at the Department of Theoretical Physics of Moscow State University.
Relativistic Lagrangian displacement field and tensor perturbations
Cornelius Rampf; Alexander Wiegand
2014-12-14
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 non-perturbative approach based on the 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 non-perturbative 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 non-propagating tensor artefacts 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 non-linear frame-dragging. We apply our findings to calculate for the first time the relativistic displacement field, up to second order, for a $\\Lambda$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.
ELKO Spinor Fields: Lagrangians for Gravity derived from Supergravity
da Rocha, Roldao
2009-01-01
Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belong -- together with Majorana spinor fields -- to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class-(5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three respectively corresponding to flagpole, flag-dipole and Weyl spinor fields. Using the mapping from ELKO spinor fields to the three classes Dirac spinor fields, it is shown that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for supergravity. The Holst action is related to the Ashtekar's quantum gravity formulation. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. Furthermore ...
Polysymplectic Hamiltonian Field Theory
G. Sardanashvily
2015-05-06
Applied to field theory, the familiar symplectic technique leads to instantaneous Hamiltonian formalism on an infinite-dimensional phase space. A true Hamiltonian partner of first order Lagrangian theory on fibre bundles $Y\\to X$ is covariant Hamiltonian formalism in different variants, where momenta correspond to derivatives of fields relative to all coordinates on $X$. We follow polysymplectic (PS) Hamiltonian formalism on a Legendre bundle over $Y$ provided with a polysymplectic $TX$-valued form. If $X=\\mathbb R$, this is a case of time-dependent non-relativistic mechanics. PS Hamiltonian formalism is equivalent to the Lagrangian one if Lagrangians are hyperregular. A non-regular Lagrangian however leads to constraints and requires a set of associated Hamiltonians. We state comprehensive relations between Lagrangian and PS Hamiltonian theories in a case of semiregular and almost regular Lagrangians. Quadratic Lagrangian and PS Hamiltonian systems, e.g. Yang - Mills gauge theory are studied in detail. Quantum PS Hamiltonian field theory can be developed in the frameworks both of familiar functional integral quantization and quantization of the PS bracket.
ELKO Spinor Fields: Lagrangians for Gravity derived from Supergravity
Roldao da Rocha; J. M. Hoff da Silva
2009-01-07
Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belong -- together with Majorana spinor fields -- to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class-(5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three respectively corresponding to flagpole, flag-dipole and Weyl spinor fields. Using the mapping from ELKO spinor fields to the three classes Dirac spinor fields, it is shown that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for supergravity. The Holst action is related to the Ashtekar's quantum gravity formulation. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. Furthermore we consider the necessary and sufficient conditions to map Dirac spinor fields (DSFs) to ELKO, in order to naturally extend the Standard Model to spinor fields possessing mass dimension one. As ELKO is a prime candidate to describe dark matter and can be obtained from the DSFs, via a mapping explicitly constructed that does not preserve spinor field classes, we prove that in particular the Einstein-Hilbert, Einstein-Palatini, and Holst actions can be derived from the QSL, as a fundamental Lagrangian for supergravity, via ELKO spinor fields. The geometric meaning of the mass dimension-transmuting operator - leading ELKO Lagrangian into the Dirac Lagrangian - is also pointed out, together with its relationship to the instanton Hopf fibration.
Recursive Solutions of Lagrangian Perturbation Theory
Matsubara, Takahiko
2015-01-01
In the standard perturbation theory (SPT) of self-gravitating Newtonian fluid in an expanding universe, recurrence relations for the solutions of higher-order perturbations are known and play an important role in practice. The recurrence relations in Lagrangian perturbation theory (LPT), however, have not been known for a long time, except a hybrid method in which solutions of LPT are derived from the recursive solutions of SPT. In this paper, monolithic recurrence relations in LPT, without referring to the results of SPT, are obtained for the first time. Recursive solutions of LPT can be derived up to any order of perturbations.
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.
Lagrangian reconstruction of cosmic velocity fields
G. Lavaux
2008-01-28
We discuss a Lagrangian reconstruction method of the velocity field from galaxy redshift catalog that takes its root in the Euler equation. This results in a ``functional'' of the velocity field which must be minimized. This is helped by an algorithm solving the minimization of cost-flow problems. The results obtained by applying this method to cosmological problems are shown and boundary effects happening in real observational cases are then discussed. Finally, a statistical model of the errors made by the reconstruction method is proposed.
Using Lagrangian perturbation theory for precision cosmology
Sugiyama, Naonori S., E-mail: nao.s.sugiyama@gmail.com [Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544-1001 (United States); Astronomical Institute, Tohoku University, 6-3, Aramakijiaoba, Sendai 980-8578 (Japan)
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%.
Application of Kawaguchi Lagrangian formulation to string theory
Yahagi, Ryoko
2015-01-01
String-scalar duality proposed by Y. Hosotani and membrane-scalar duality by A. Sugamoto are reexamined in the context of Kawaguchi Lagrangian formulation. The characteristic feature of this formulation is the indifferent nature of fields and parameters. Therefore even the exchange of roles between fields and parameters is possible. In this manner, dualities above can be proved easily. A challenging problem of compactification in superstring theory is also studied in this formulation. A replacement of the role of Grassmann parameters of the 2-dimensional superspace by the 9th component of Neveu-Schwarz-Ramond (NSR) fermions gives a compactified superstring model in the 9th direction. This is an example of the exchange between fermionic fields and parameters.
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.
Topics in low-dimensional field theory
Crescimanno, M.J.
1991-04-30
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density.
Quaternionic quantum field theory
Adler, S.L.
1985-08-19
We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second-order wave equation. The theory is initially defined in terms of a quaternion-imaginary Lagrangian using the Feynman sum over histories. A Schroedinger equation can be derived from the functional integral, which identifies the quaternion-imaginary quantum Hamiltonian. Conversely, the transformation theory based on this Hamiltonian can be used to rederive the functional-integral formulation.
Effective metric Lagrangians from an underlying theory with two propagating degrees of freedom
Krasnov, Kirill [School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD (United Kingdom)
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.
Renormalization and quantum field theory
R. E. Borcherds
2011-03-09
The aim of this paper is to describe how to use regularization and renormalization to construct a perturbative quantum field theory from a Lagrangian. We first define renormalizations and Feynman measures, and show that although there need not exist a canonical Feynman measure, there is a canonical orbit of Feynman measures under renormalization. We then construct a perturbative quantum field theory from a Lagrangian and a Feynman measure, and show that it satisfies perturbative analogues of the Wightman axioms, extended to allow time-ordered composite operators over curved spacetimes.
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.
a Note on the - Invariant Lagrangian Densities for the Free Abelian 2-FORM Gauge Theory
NASA Astrophysics Data System (ADS)
Gupta, Saurabh; Malik, R. P.
We show that the previously known off-shell nilpotent (s(a)b2 = 0) and absolutely anticommuting (sb sab + sab sb = 0) Becchi-Rouet-Stora-Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3+1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci-Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler-Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s(a)b. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.
Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
Solomon, Jake P. (Jake Philip)
2006-01-01
We define a new family of open Gromov-Witten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian ...
Regular hyperbolicity, dominant energy condition and causality for Lagrangian theory of maps
Willie Wai-Yeung Wong
2011-05-16
The goal of the present paper is three-fold. First is to clarify the connection between the dominant energy condition and hyperbolicity properties of Lagrangian field theories. Second is to provide further analysis on the breakdown of hyperbolicity for the Skyrme model, sharpening the results of Crutchfield and Bell and comparing against a result of Gibbons, and provide a local well-posedness result for the dynamical problem in the Skyrme model. Third is to provide a short summary of the framework of regular hyperbolicity of Christodoulou for the relativity community. In the process, a general theorem about dominant energy conditions for Lagrangian theories of maps is proved, as well as several results concerning hyperbolicity of those maps.
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. [Departamento de Fisica Teorica, Universidad de Zaragoza, Zaragoza 50009 (Spain)
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.
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.
Infinite class of PT-symmetric theories from one timelike Liouville Lagrangian.
Bender, Carl M; Hook, Daniel W; Mavromatos, Nick E; Sarkar, Sarben
2014-12-01
Logarithmic timelike Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field ?. In Euclidean space, the Lagrangian of such a theory L=1/2(??)^{2}-ig?exp(ia?) is analyzed using the techniques of PT-symmetric quantum theory. It is shown that L defines an infinite number of unitarily inequivalent sectors of the theory labeled by the integer n. In one-dimensional space (quantum mechanics), the energy spectrum is calculated in the semiclassical limit and the mth energy level in the nth sector is given by E_{m,n}?(m+1/2)^{2}a^{2}/(16n^{2}). PMID:25526116
Holography and defect conformal field theories
Oliver Dewolfe; Daniel Z. Freedman; Hirosi Ooguri
2002-01-01
We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS5×S5 bisected by an AdS4×S2 ``brane,'' is dual to N=4 super Yang-Mills theory in R4 coupled to an R3 defect. We propose a complete Lagrangian for the field theory dual, a novel
Quantum field theory and the Standard Model
W. Hollik
2010-12-17
In this lecture we discuss the basic ingredients for gauge invariant quantum field theories. We give an introduction to the elements of quantum field theory, to the construction of the basic Lagrangian for a general gauge theory, and proceed with the formulation of QCD and the electroweak Standard Model with electroweak symmetry breaking via the Higgs mechanism. The phenomenology of W and Z bosons is discussed and implications for the Higgs boson are derived from comparison with experimental precision data.
Lagrangian Theory for 3D Vortex Sheets with Axial or Helical Symmetry
Caflisch, Russel
equations for flow due to a vortex sheet. A "Lagrangian" description of the motion of S is given in termsLagrangian Theory for 3D Vortex Sheets with Axial or Helical Symmetry Russel E. Caflisch and Xiao a three-dimensional vortex sheet in inviscid, incompressible flow which is irrotational away from
Lagrangian Theory for 3D Vortex Sheets with Axial or Helical Symmetry
Li, Xiaofan
; These are the Eulerian equations for ow due to a vortex sheet. A \\Lagrangian" description of the motion of S is givenLagrangian Theory for 3D Vortex Sheets with Axial or Helical Symmetry #3; Russel E. Ca isch Consider a three-dimensional vortex sheet in inviscid, incompressible ow which is irrotational away from
Lagrangian perturbation theory at one loop order: Successes, failures, and improvements
NASA Astrophysics Data System (ADS)
Vlah, Zvonimir; Seljak, Uroš; Baldauf, Tobias
2015-01-01
We apply the convolved Lagrangian perturbation theory (CLPT) formalism, in which one can express the matter density power spectrum in terms of integrals over a function of cumulants of the displacement field, allowing for a resummation of the terms, to evaluate the full one loop power spectrum. We keep the cumulants up to third order, extending the Zel'dovich approximation and providing the power spectrum analogous to the calculations recently performed for the correlation function. We compare the results to the N-body simulations and to the Lagrangian perturbation simulations up to the second order. We find that the analytic calculations are in a good agreement with the Lagrangian perturbation theory simulations, but when compared to full N-body simulations, we find that, while one loop calculations improve upon the Zel'dovich approximation in the power spectrum, they still significantly lack power. As found previously in the correlation function one loop CLPT improves slightly against Zel'dovich above 30 Mpc /h but is actually worse than Zel'dovich below that. We investigate the deficiencies of the CLPT approach and argue that main problem of CLPT is its inability to trap particles inside dark matter halos, which leads to an overestimate of the small-scale power of the displacement field and to an underestimate of the small-scale power from one halo term effects. We model this using the displacement field damped at a nonlinear scale (CLPTs). To explore this in more detail we decompose the power spectrum and correlation function into three additive components: Zel'dovich, residual baryon acoustic oscillation (BAO) wiggle, and residual broadband. One loop CLPT predicts small modifications to BAO wiggles that are enhanced in CLPTs, with up to 5% corrections to correlation function around BAO scale. For the residual broadband contribution CLPTs improves the broadband power in the power spectrum but is still insufficient compared to simulations and makes the correlation function agreement worse than CLPT.
NASA Astrophysics Data System (ADS)
Buchbinder, I. L.; Krykhtin, V. A.; Tsulaia, M.
2015-07-01
We consider massive half-integer higher spin fields coupled to an external constant electromagnetic field in flat space of an arbitrary dimension and construct a gauge invariant Lagrangian in the linear approximation in the external field. A procedure for finding the gauge-invariant Lagrangians is based on the BRST construction where no off-shell constraints on the fields and on the gauge parameters are imposed from the very beginning. As an example of the general procedure, we derive a gauge invariant Lagrangian for a massive fermionic field with spin 3/2 which contains a set of auxiliary fields and gauge symmetries.
I. L. Buchbinder; V. A. Krykhtin; M. Tsulaia
2015-01-14
We consider massive half-integer higher spin fields coupled to an external constant electromagnetic field in flat space of an arbitrary dimension and construct a gauge invariant Lagrangian in the linear approximation in the external field. A procedure for finding the gauge-invariant Lagrangians is based on the BRST construction where no off-shell constraints on the fields and on the gauge parameters are imposed from the very beginning. As an example of the general procedure, we derive a gauge invariant Lagrangian for a massive fermionic field with spin 3/2 which contains a set of auxiliary fields and gauge symmetries.
About non standard Lagrangians in cosmology
Dimitrijevic, Dragoljub D.; Milosevic, Milan [Department of Physics, Faculty of Science and Mathematics, University of Nis, Visegradska 33, P.O. Box 224, 18000 Nis (Serbia)
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.
Cosmological status of Lagrangian theory of density perturbations
V. Strokov
2006-12-14
We show that hydrodynamical and field approaches in theory of cosmological scalar perturbations are equivalent for a single medium. We also give relations between notations introduced by V. Lukash, J. Bardeen, J. Bardeen et al. and G. Chibisov and V. Mukhanov.
NASA Astrophysics Data System (ADS)
Buchbinder, I. L.; Reshetnyak, A.
2012-09-01
We construct a Lagrangian description of irreducible integer higher spin representations of the Poincaré-group with an arbitrary Young tableaux having k rows, on a basis of the universal BRST approach. Starting with a description of bosonic mixed-symmetry higher spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with special Poincaré module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincaré-group representations) into a first-class constraint system. For this purpose, we find, for the first time, auxiliary representations of the constraint subalgebra, to be isomorphic due to Howe duality to sp(2k) algebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We propose a universal procedure of constructing unconstrained gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive bosonic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincaré-group representation. As examples of the general procedure, we formulate the method of Lagrangian construction for bosonic fields subject to arbitrary Young tableaux having 3 rows and derive the gauge-invariant Lagrangian for new model of massless rank-4 tensor field with spin (2,1,1) and second stage reducible gauge symmetries.
Tulczyjew triples: from statics to field theory
Katarzyna Grabowska; Janusz Grabowski
2014-01-18
We propose a geometric approach to dynamical equations of physics, based on the idea of the Tulczyjew triple. We show the evolution of these concepts, starting with the roots lying in the variational calculus for statics, through Lagrangian and Hamiltonian mechanics, and concluding with Tulczyjew triples for classical field theories, illustrated with a numer of important examples.
Chiral Lagrangians for Baryons Coupled to Massive SPIN-1 Fields
NASA Astrophysics Data System (ADS)
Borasoy, B.; Meißner, Ulf-G.
We analyze the effective low energy field theory of Goldstone bosons and baryons chirally coupled to massive spin-1 fields. We use the electromagnetic baryon form factors to demonstrate the formal equivalence between the vector and the tensor field formulation for the spin-1 fields. We also discuss the origin of the so-called Weinberg term in pion-nucleon scattering and the role of ? meson exchange. Chirally coupled vector mesons do not give rise to this two-pion nucleon seagull interaction but rather to higher order corrections. Some problems of the formal equivalence arising in higher orders and related to loops are touched upon.
Washington Taylor
2006-06-28
This elementary introduction to string field theory highlights the features and the limitations of this approach to quantum gravity as it is currently understood. String field theory is a formulation of string theory as a field theory in space-time with an infinite number of massive fields. Although existing constructions of string field theory require expanding around a fixed choice of space-time background, the theory is in principle background-independent, in the sense that different backgrounds can be realized as different field configurations in the theory. String field theory is the only string formalism developed so far which, in principle, has the potential to systematically address questions involving multiple asymptotically distinct string backgrounds. Thus, although it is not yet well defined as a quantum theory, string field theory may eventually be helpful for understanding questions related to cosmology in string theory.
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.
Lagrangian perturbation theory for a superfluid immersed in an elastic neutron star crust
N. Andersson; B. Haskell; L. Samuelsson
2011-05-06
The inner crust of mature neutron stars, where an elastic lattice of neutron-rich nuclei coexists with a neutron superfluid, impacts on a range of astrophysical phenomena. The presence of the superfluid is key to our understanding of pulsar glitches, and is expected to affect the thermal conductivity and hence the evolution of the surface temperature. The coupling between crust and superfluid must also be accounted for in studies of neutron star dynamics, discussions of global oscillations and associated instabilities. In this paper we develop Lagrangian perturbation theory for this problem, paying attention to key issues like superfluid entrainment, potential vortex pinning, dissipative mutual friction and the star's magnetic field. We also discuss the nature of the core-crust interface. The results provide a theoretical foundation for a range of interesting astrophysical applications.
The Lagrangian formulation of strong-field quantum electrodynamics in a plasma
Raicher, Erez, E-mail: erez.raicher@mail.huji.ac.il [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel) [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel); Department of Applied Physics, Soreq Nuclear Research Center, Yavne 81800 (Israel); Eliezer, Shalom [Department of Applied Physics, Soreq Nuclear Research Center, Yavne 81800 (Israel) [Department of Applied Physics, Soreq Nuclear Research Center, Yavne 81800 (Israel); Nuclear Fusion Institute, Polytechnic University of Madrid, Madrid (Spain); Zigler, Arie [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)] [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)
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.
NASA Astrophysics Data System (ADS)
Reshetnyak, A.
2013-04-01
We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having k rows, on a basis of the BRST-BFV approach suggested for bosonic fields in our first article [I.L. Buchbinder, A. Reshetnyak, Nucl. Phys. B 862 (2012) 270, arXiv:1110.5044 [hep-th
Tatekawa, Takayuki, E-mail: tatekawa@akane.waseda.jp [Center for Information initiative, 3-9-1 Bunkyo, Fukui, 910-8709 JAPAN (Japan)
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.
On background-independent open-string field theory
Edward Witten
1992-01-01
A framework for background-independent open-string field theory is proposed. The approach involves using the Batalin-Vilkovisky formalism, in a way suggested by recent developments in closed-string field theory, to implicitly define a gauge-invariant Lagrangian in a hypothetical ``space of all open-string world-sheet theories.'' It is built into the formalism that classical solutions of the string field theory are Becchi-Rouet-Stora-Tyutin- (BRST-) invariant
Euler-Poincare reduction for discrete field theories
Vankerschaver, Joris [Department of Mathematical Physics and Astronomy, University of Ghent, Krijgslaan 281, B-9000 Ghent (Belgium)
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.
Euler-Poincare reduction for discrete field theories
Joris Vankerschaver
2007-03-29
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.
On exact tachyon potential in open string field theory
Anton A. Gerasimov; Samson L. Shatashvili
2000-01-01
In these notes we revisit the tachyon lagrangian in the open string field theory using background independent approach of Witten from 1992. We claim that the tree level lagrangian (up to second order in derivatives and modulo some class of field redefinitions) is given by L = e-T(partialT)2+(1+T)e-T. Upon obvious change of variables this leads to the potential energy -phi2log
Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory
Andreussi, T. [Alta S.p.A., Pisa 56121 (Italy)] [Alta S.p.A., Pisa 56121 (Italy); Morrison, P. J. [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, Texas 78712-1060 (United States)] [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, Texas 78712-1060 (United States); Pegoraro, F. [Università di Pisa, Dipartimento di Fisica E. Fermi, Pisa 56127 (Italy)] [Università di Pisa, Dipartimento di Fisica E. Fermi, Pisa 56127 (Italy)
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.
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.
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.
Field theory of monochromatic optical beams. I
Aiello, Andrea
2014-01-01
We study monochromatic, scalar solutions of the Helmholtz and paraxial wave equations from a field-theoretic point of view. We introduce appropriate time-independent Lagrangian densities for which the Euler-Lagrange equations reproduces either Helmholtz and paraxial wave equations with the $z$-coordinate, associated with the main direction of propagation of the fields, playing the same role of time in standard Lagrangian theory. For both Helmholtz and paraxial scalar fields, we calculate the canonical energy-momentum tensor and determine the continuity equations relating "energy" and "momentum" of the fields. Eventually, the reduction of the Helmholtz wave equation to a useful first-order Dirac form, is presented. This work sheds some light on the intriguing and not so acknowledged connections between angular spectrum representation of optical wavefields, cosmological models and physics of black holes.
Field theory of monochromatic optical beams. I
Andrea Aiello
2014-12-02
We study monochromatic, scalar solutions of the Helmholtz and paraxial wave equations from a field-theoretic point of view. We introduce appropriate time-independent Lagrangian densities for which the Euler-Lagrange equations reproduces either Helmholtz and paraxial wave equations with the $z$-coordinate, associated with the main direction of propagation of the fields, playing the same role of time in standard Lagrangian theory. For both Helmholtz and paraxial scalar fields, we calculate the canonical energy-momentum tensor and determine the continuity equations relating "energy" and "momentum" of the fields. Eventually, the reduction of the Helmholtz wave equation to a useful first-order Dirac form, is presented. This work sheds some light on the intriguing and not so acknowledged connections between angular spectrum representation of optical wavefields, cosmological models and physics of black holes.
Lagrangian and Hamiltonian formalism for discontinuous fluid and gravitational field
NASA Astrophysics Data System (ADS)
Hájí?ek, P.; Kijowski, J.
1998-01-01
The barotropic ideal fluid with step and ?-function discontinuities coupled to Einstein's gravity is studied. The discontinuities represent star surfaces and thin shells; only nonintersecting discontinuity hypersurfaces are considered. No symmetry (such as, e.g., the spherical symmetry) is assumed. The symplectic structure as well as the Lagrangian and the Hamiltonian variational principles for the system are written down. The dynamics is described completely by the fluid variables and the metric on the fixed background manifold. The Lagrangian and the Hamiltonian are given in two forms: the volume form, which is identical to that corresponding to the smooth system, but employs distributions, and the surface form, which is a sum of volume and surface integrals and employs only smooth variables. The surface form is completely four or three covariant (unlike the volume form). The spacelike surfaces of time foliations can have a cusp at the surface of discontinuity. Geometrical meaning of the surface terms in the Hamiltonian is given. Some of the constraint functions that result from the shell Hamiltonian cannot be smeared so as to become differentiable functions on the (unconstrained) phase space. Generalization of the formulas to more general fluid is straightforward.
Quantum Field Theory and Representation Theory
Woit, Peter
Quantum Field Theory and Representation Theory Peter Woit woit@math.columbia.edu Department of Mathematics Columbia University Quantum Field Theory and Representation Theory p.1 #12;Outline of the talk · Quantum Mechanics and Representation Theory: Some History Quantum Field Theory and Representation Theory
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.
Transport induced by mean-eddy interaction: I. Theory, and relation to Lagrangian lobe dynamics
NASA Astrophysics Data System (ADS)
Ide, Kayo; Wiggins, Stephen
2015-02-01
In this paper we develop a method for the estimation of Transport Induced by the Mean-Eddy interaction (TIME) in two-dimensional unsteady flows. The method is based on the dynamical systems approach to fluid transport and can be viewed as a hybrid combination of Lagrangian and Eulerian methods. The (Eulerian) boundaries across which we consider (Lagrangian) transport are kinematically defined by appropriately chosen streamlines of the mean flow. By evaluating the impact of the mean-eddy interaction on transport, the TIME method can be used as a diagnostic tool for transport processes that occur during a specified time interval along a specified boundary segment. We introduce two types of TIME functions: one that quantifies the accumulation of flow properties and another that measures the displacement of the transport geometry. The spatial geometry of transport is described by the so-called pseudo-lobes, and temporal evolution of transport by their dynamics. In the case where the TIME functions are evaluated along a separatrix, the pseudo-lobes have a relationship to the lobes of Lagrangian transport theory. In fact, one of the TIME functions is identical to the Melnikov function that is used to measure the distance, at leading order in a small parameter, between the two invariant manifolds that define the Lagrangian lobes. We contrast the similarities and differences between the TIME and Lagrangian lobe dynamics in detail. An application of the TIME method is carried out for inter-gyre transport in the wind-driven oceanic circulation model and a comparison with the Lagrangian transport theory is made.
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.
Closed-form weak-field expansion of two-loop Euler-Heisenberg Lagrangians
G. V. Dunne; A. Huet; D. Rivera; C. Schubert
2006-09-10
We obtain closed-form expressions, in terms of the Faulhaber numbers, for the weak-field expansion coefficients of the two-loop Euler-Heisenberg effective Lagrangians in a magnetic or electric field. This follows from the observation that the magnetic worldline Green's function has a natural expansion in terms of the Faulhaber numbers.
Hamilton-Jacobi theory in multisymplectic classical field theories
Manuel de León; Pedro Daniel Prieto-Martínez; Narciso Román-Roy; Silvia Vilariño
2015-04-08
The geometric framework for the Hamilton-Jacobi theory developed in previous works is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.
California at Santa Cruz, University of
1 Complex representations of scalar fields Let # i (x) be a set of n complex scalar fields. The scalar Lagrangian L = 1 2 (# µ # i ) + (# µ # i ) - V (# i , # + i ) (1) is assumed to be invariant under a compact symmetry group G, under which the scalar fields transform as: # i # U i j # j , # + i # # + j (U
Quantum Field Perturbation Theory Revised
Marco Matone
2015-07-27
Schwinger's trick in quantum field theory can be easily implemented in the case of scalar theories in D-dimension, with exponential interactions, such as $\\mu^D\\exp(\\alpha\\phi)$. The key point is the relation $$ \\exp\\big(\\alpha{\\delta\\over \\delta J(x)}\\big)\\exp(-Z_0[J])=\\exp(-Z_0[J+\\alpha_x]) $$ with $J$ the external source, and $\\alpha_x(y)=\\alpha\\delta(y-x)$. Such a shift, related to the normal ordering of $\\exp(\\alpha\\phi)$, leads to an exact scaling relation by renormalizing $\\mu$. The theory exhibits spontaneous symmetry breaking of space-time translations, due to the fact that the vacuum is filled in by infinitely many point-like sources $\\alpha_x(y)$. This suggests that the vev of the energy-momentum tensor of the purely scalar part of the Higgs lagrangian, proposed in arXiv:1506.05761, may explain the origin of the cosmological constant. In this respect, we derive the expression of $\\langle\\phi(x)\\rangle$, compute its space-time integral, and prove that $x$-dependent contributions to $\\langle\\phi(x)\\rangle$ start only at $\\alpha^5$. Next, we derive a new formulation of perturbation theory for the potentials $V(\\phi)=\\lambda:\\phi^n:$, using the partition function associated to $:\\exp(\\alpha\\phi):$. The $\\Delta_F(0)$ related to the normal ordering are absorbed at once. The functional derivatives with respect to $J$ are explicitly computed and the Green's functions are expressed in terms of combinatorics involving ordinary derivatives. Finally, we note that the Feynman propagator can be seen as building block for a metric on suitable moduli spaces. In the two-dimensional case, this shows a connection with the moduli space of punctured spheres and with the underlying Liouville theory. The present investigation can be extended to more general quantum field theories.
NASA Astrophysics Data System (ADS)
Katz, Joseph; Livshits, Gideon I.
2008-09-01
The prescription of Silva to derive superpotential equations from variational derivatives rather than from Lagrangian densities is applied to theories of gravity derived from Lovelock Lagrangians in the Palatini representation. Spacetimes are without torsion and isolated sources of gravity are minimally coupled. On a closed boundary of spacetime, the metric is given and the connection coefficients are those of Christoffel. We derive equations for the superpotentials in these conditions. The equations are easily integrated and we give the general expression for all superpotentials associated with Lovelock Lagrangians. We find, in particular, that in Einstein's theory, in any number of dimensions, the superpotential, valid at spatial and at null infinity, is that of Katz, Bi?ák and Lynden-Bell, the KBL superpotential. We also give explicitly the superpotential for Gauss Bonnet theories of gravity. Finally, we find a simple expression for the superpotential of Einstein Gauss Bonnet theories with an anti-de Sitter background: it is minus the KBL superpotential, confirming, as it should, the calculation of the total mass energy of spacetime at spatial infinity by Deser and Tekin.
Thomas Buchert; Matthias Ostermann
2012-07-05
In this first paper we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a self-contained derivation of a general-relativistic analogue of Zel'dovich's approximation for the description of structure formation in cosmology, and compare it with previous suggestions in the literature. This approximation is then investigated: paraphrasing the derivation in the Newtonian framework we provide general-relativistic analogues of the basic system of equations for a single dynamical field variable and recall the first-order perturbation solution of these equations. We then define a general-relativistic analogue of Zel'dovich's approximation and investigate its implications by functionally evaluating relevant variables, and we address the singularity problem. We so obtain a possibly powerful model that, although constructed through extrapolation of a perturbative solution, can be used to put into practice nonperturbatively, e.g. problems of structure formation, backreaction problems, nonlinear properties of gravitational radiation, and light-propagation in realistic inhomogeneous universe models. With this model we also provide the key-building blocks for initializing a fully relativistic numerical simulation.
Ning Wu
1998-06-03
In this paper, we will construct a gauge field model, in which the masses of gauge fields are non-zero and the local gauge symmetry is strictly preserved. A SU(N) gauge field model is discussed in details in this paper. In the limit $\\alpha \\longrightarrow 0$ or $\\alpha \\longrightarrow \\infty$, the gauge field model discussed in this paper will return to Yang-Mills gauge field model. This theory could be regarded as theoretical development of Yang-Mills gauge field theory.
(Non-)Decoupled Supersymmetric Field Theories
Di Pietro, Lorenzo; Komargodski, Zohar
2014-01-01
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, 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 ${\\cal N}$ = 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 ...
Augmented Lagrangian Method for Constrained Nuclear Density Functional Theory
A. Staszczak; M. Stoitsov; A. Baran; W. Nazarewicz
2010-07-21
The augmented Lagrangiam 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.
Zacharias A. M. Protogeros; Adrian L. Melott; Robert J. Scherrer
1996-11-20
We test tree-level perturbation theory for Gaussian initial conditions with power spectra $P(k)\\propto k^n$ by comparing the probability distribution function (PDF) for the density predicted by the Local Lagrangian Approximation (LLA) with the results of numerical gravitational clustering simulations. Our results indicate that our approximation correctly reproduces the evolved density PDF for $-3 \\leq n \\leq-1$ power spectra up to the weakly nonlinear regime, while it shows marginal agreement for power indices n=0 and +1 in the linear regime and poor agreement beyond this point. This suggests that tree-level perturbation theory (as realized in the Local Lagrangian Approximation) can accurately predict the density distribution function for $-3 \\leq n \\leq -1$ but fails for $n \\ge 0$.
Lagrangian derivation of the two coupled field equations in the Janus cosmological model
NASA Astrophysics Data System (ADS)
Petit, Jean-Pierre; D'Agostini, G.
2015-05-01
After a review citing the results obtained in previous articles introducing the Janus Cosmological Model, consisting of a set of two coupled field equations, where one metrics refers to the positive masses and the other to the negative masses, which explains the observed cosmic acceleration and the nature of dark energy, we present the Lagrangian derivation of the model.
Semi-Lagrangian schemes with field aligned interpolation for ion turbulence simulations in a
Mehrenberger, Michel
Fourier filtering : ORB/NEMORB/EUTERPE (PIC code) Global field aligned mesh : XGC1 (PIC code) Flux tube approximation : GENE (Eulerian code ; local and global version) How to deal with GYSELA (global semi-Lagrangian code) ? curvilinear mesh / optimal choice of the points Warning : stretched mesh can lead to numerical
A phenomenological theory of Eulerian and Lagrangian velocity fluctuations in turbulent flows
Laurent Chevillard; Bernard Castaing; Alain Arneodo; Emmanuel Leveque; Jean-Francois Pinton; Stephane Roux
2012-12-03
A phenomenological theory of the fluctuations of velocity occurring in a fully developed homogeneous and isotropic turbulent flow is presented. The focus is made on the fluctuations of the spatial (Eulerian) and temporal (Lagrangian) velocity increments. The universal nature of the intermittency phenomenon as observed in experimental measurements and numerical simulations is shown to be fully taken into account by the multiscale picture proposed by the multifractal formalism, and its extensions to the dissipative scales and to the Lagrangian framework. The article is devoted to the presentation of these arguments and to their comparisons against empirical data. In particular, explicit predictions of the statistics, such as probability density functions and high order moments, of the velocity gradients and acceleration are derived. In the Eulerian framework, at a given Reynolds number, they are shown to depend on a single parameter function called the singularity spectrum and to a universal constant governing the transition between the inertial and dissipative ranges. The Lagrangian singularity spectrum compares well with its Eulerian counterpart by a transformation based on incompressibility, homogeneity and isotropy and the remaining constant is shown to be difficult to estimate on empirical data. It is finally underlined the limitations of the increment to quantify accurately the singular nature of Lagrangian velocity. This is confirmed using higher order increments unbiased by the presence of linear trends, as they are observed on velocity along a trajectory.
Reduced classical field theories. k-cosymplectic formalism on Lie algebroids
D. Martin de Diego; S. Vilariñ o
2010-01-07
In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of $k$-cosymplectic geometry. We discuss the relation between Lagrangian and Hamiltonian descriptions through a convenient notion of Legendre transformation. The theory is a natural generalization of the standard one; in addition, other interesting examples are studied, mainly on reduction of classical field theories.
Covariantizing Classical Field Theories
Marco Castrillón López; Mark J. Gotay
2010-08-18
We show how to enlarge the covariance group of any classical field theory in such a way that the resulting "covariantized" theory is 'essentially equivalent' to the original. In particular, our technique will render any classical field theory generally covariant, that is, the covariantized theory will be spacetime diffeomorphism-covariant and free of absolute objects. Our results thus generalize the well-known parametrization technique of Dirac and Kucha\\v{r}. Our constructions apply equally well to internal covariance groups, in which context they produce natural derivations of both the Utiyama minimal coupling and St\\"uckelberg tricks.
Effective field theory for proton halo nuclei
Emil Ryberg; Christian Forssén; H. -W. Hammer; Lucas Platter
2013-08-27
We use halo effective field theory to analyze the universal features of proton halo nuclei bound due to a large S-wave scattering length. With a Lagrangian built from effective core and valence-proton fields, we derive a leading-order expression for the charge form factor. Within the same framework we also calculate the radiative proton capture cross section. Our general results at leading order are applied to study the excited 1/2+ state of Fluorine-17, and we give results for the charge radius and the astrophysical S-factor.
Effective field theory for proton halo nuclei
Ryberg, Emil; Hammer, H -W; Platter, Lucas
2014-01-01
We use halo effective field theory to analyze the universal features of proton halo nuclei bound due to a large S-wave scattering length. With a Lagrangian built from effective core and valence-proton fields, we derive a leading-order expression for the charge form factor. Within the same framework we also calculate the radiative proton capture cross section. Our general results at leading order are applied to study the excited 1/2+ state of Fluorine-17, and we give results for the charge radius and the astrophysical S-factor.
Euler-Heisenberg Lagrangian to all orders in the magnetic field and the Chiral Magnetic Effect
Simon Wolfgang Mages; Matthias Aicher; Andreas Schäfer
2010-09-08
In high energy heavy ion collisions as well as in astrophysical objects like magnetars extreme magnetic field strengths are reached. Thus, there exists a need to calculate divers QED processes to all orders in the magnetic field. We calculate the vacuum polarization graph in second order of the electric field and all orders of the magnetic field resulting in a generalization of the Euler-Heisenberg Lagrangian. We perform the calculation in the effective Lagrangian approach of J. Schwinger as well as using modified Feynman rules. We find that both approaches give the same results provided that the different finite renormalization terms are taken into account. Our results imply that any quantitative explanation of the recently proposed Chiral Magnetic Effect has to take 'Strong QED' effects into account, because these corrections are huge.
(Non-)Decoupled Supersymmetric Field Theories
Lorenzo Di Pietro; Michael Dine; Zohar Komargodski
2014-02-14
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, 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 ${\\cal N}$ = 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).
(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 [Institute of Physics, Pregrevica 118, Zemun, P.O. Box 57, 11001 Belgrade (Serbia)
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.
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.
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.
Free field theory at null infinity and white noise calculus: a BMS invariant dynamical system
Claudio Dappiaggi
2006-07-25
In the context of asymptotically flat spacetimes we exploit techniques proper either of white noise analysis either of dynamical systems in order to develop the Lagrangian and the Hamiltonian approach to a BMS invariant field theory at null infinity.
NASA Astrophysics Data System (ADS)
Goldman, Ron; Efrati, Shai; Lehahn, Yoav; Gertman, Isaac; Heifetz, Eyal
2014-05-01
We present a tool for daily validation of modeled or satellite derived velocity fields in the southeastern region of the Mediterranean. Within this tool, spatial patterns of Lagrangian Coherent Structures (LCS) derived from the velocity field are compared to distribution patterns of satellite derived surface chlorophyll. This comparison is advantageous to pollution spread predictions since it compares the location of fronts in passive tracer spread. The suggested methodology is based on Lagrangian tools that were shown to be very effective in reconstructing the specific effect of horizontal stirring on individual oceanic patterns. Lagrangian techniques are based, in general, on the identification of the velocity field characteristics along particle trajectories. They are well suited for diagnosing properties of tracers like chlorophyll, since they allow to quantify the dynamical properties experienced by a parcel of water during its motion. The Lagrangian diagnostics performed in this tool are based on analyzing the spatial structure of LCS from calculation of finite size Lyapunov exponents (FSLE). These LCS induce in advected tracer fields filament patterns with typical length in the range of 10 - 100 km and lifetime in the range of days/weeks (though it can be much longer if the patterns are associated to long-lived and energetic mesoscale features with low temporal variability). Since LCS represent transport barriers and tracer boundaries, they separate between water bodies with possibly different physical - biogeochemical properties. Daily analyses ( available online at http://isramar.ocean.org.il/isramar2009/cosem/fsle.aspx ) of LCS is performed on AVISO altimetry derived velocity fields and on operational numerical circulation forecasts, which are produced as part of the South Eastern Levantine Israeli Prediction System (SELIPS). The LCS analyses are then placed atop maps of surface Chlorophyll concentrations, which is provided within the MyOcean project. A subjective scoring criteria for the fit quality is formulated and implemented for a year of validating circulation estimates in the southeastern Levantine.
On Lagrangian formulations for arbitrary bosonic HS fields on Minkowski backgrounds
NASA Astrophysics Data System (ADS)
Reshetnyak, A. A.
2012-09-01
We review the details of unconstrained Lagrangian formulations for Bose particles propagated on an arbitrary dimensional flat space-time and described by the unitary irreducible integer higher-spin representations of the Poincare group subject to Young tableaux Y( s 1, ..., s k ) with k rows. The procedure is based on the construction of scalar auxiliary oscillator realizations for the symplectic sp(2 k) algebra which encodes the second-class operator constraints subsystem in the HS symmetry algebra. Application of an universal BRST approach reproduces gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive bosonic fields of any spin with appropriate number of auxiliary fields.
Bosonic String and String Field Theory: a solution using the holomorphic representation
C. G. Bollini; M. C. Rocca
2009-08-20
In this paper we show that the holomorphic representation is appropriate for description in a consistent way string and string field theories, when the considered number of component fields of the string field is finite. A new Lagrangian for the closed string is obtained and shown to be equivalent to Nambu-Goto's Lagrangian. We give the notion of anti-string, evaluate the propagator for the string field, and calculate the convolution of two of them.
Interactions from Field Theory 6.1 The Okubo Method
Fuda, Michael G.
with the operators B m tB B Bp , ,( ), b m tb b bp , ,( ), and a pg gl,( ) which are annihilation operators used for constructing mass operator interactions from effective Lagrangians. These interactions include field theory is divided into two orthogonal subspaces with projection operators h and L. The h
Information channel capacity in the field theory estimation
J. S?adkowski; J. Syska
2012-12-26
The construction of the information capacity for the vector position parameter in the Minkowskian space-time is presented. This lays the statistical foundations of the kinematical term of the Lagrangian of the physical action for many field theory models, derived by the extremal physical information method of Frieden and Soffer.
Poincare' invariance constraints on non-relativistic effective field theories
Antonio Vairo
2011-03-18
We discuss Poincare' invariance in the context of non-relativistic effective field theories of QCD. We show, in the cases of the HQET and pNRQCD, that the algebra of the generators of the Poincare' transformations imposes precise constraints on the form of the Lagrangian. In the case of the HQET they are the relations formerly obtained by reparametrization invariance.
Holography and defect conformal field theories
NASA Astrophysics Data System (ADS)
Dewolfe, Oliver; Freedman, Daniel Z.; Ooguri, Hirosi
2002-07-01
We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS5×S5 bisected by an AdS4×S2 ``brane,'' is dual to N=4 super Yang-Mills theory in R4 coupled to an R3 defect. We propose a complete Lagrangian for the field theory dual, a novel ``defect superconformal field theory'' wherein a subset of the fields of N=4 SYM theory interacts with a d=3 SU(N) fundamental hypermultiplet on the defect preserving conformal invariance and 8 supercharges. The Kaluza-Klein reduction of wrapped D5 modes on AdS4×S2 leads to towers of short representations of OSp(4|4), and we construct the map to a set of dual gauge-invariant defect operators O3 possessing integer conformal dimensions. Gravity calculations of
Vakonomic Constraints in Higher-Order Classical Field Theory
NASA Astrophysics Data System (ADS)
Campos, Cédric M.
2010-07-01
We propose a differential-geometric setting for the dynamics of a higher-order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both, the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher-order jet bundle and the canonical multisymplectic form on its affine dual. The result is that we obtain a unique and global intrinsic description of the dynamics. The case of vakonomic constraints is also studied within this formalism.
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.
Algebraic Quantum Field Theory
Hans Halvorson; Michael Mueger
2006-02-14
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by S. Doplicher, R. Haag, and J. E. Roberts (DHR); and we give an alternative proof of Doplicher and Roberts' reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix.
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.
Walter F. Wreszinski; Luiz A. Manzoni; Oscar Bolinaa
We prove the existence of the Bogoliubov S(g) operator for the (: ?4 :)2 quantum field theory for coupling functions g of compact support in space and time. The construction is nonperturbative and relies on a theorem of Kisynski. It implies almost automatically the properties of unitarity and causality for disjoint supports in the time variable.
Antonio Pich
1998-01-01
These lectures provide an introduction to the basic ideas and methods of Effective Field Theory, and a description of a few interesting phenomenological applications in particle physics. The main conceptual foundations are discussed in sections 2 and 3, which cover the momentum expansion and the most important issues associated with the renormalization process. Section 4 presents an overview of Chiral
NASA Astrophysics Data System (ADS)
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.
Subedi, P.; Chhiber, R.; Tessein, J. A.; Wan, M.; Matthaeus, W. H. [Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 (United States)
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.
Linear Stability of Elliptic Lagrangian Solutions of the Planar Three-Body Problem via Index Theory
NASA Astrophysics Data System (ADS)
Hu, Xijun; Long, Yiming; Sun, Shanzhong
2014-09-01
It is well known that the linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three-body problem depends on the mass parameter and the eccentricity . We are not aware of any existing analytical method which relates the linear stability of these solutions to the two parameters directly in the full rectangle [0, 9] × [0, 1), aside from perturbation methods for e > 0 small enough, blow-up techniques for e sufficiently close to 1, and numerical studies. In this paper, we introduce a new rigorous analytical method to study the linear stability of these solutions in terms of the two parameters in the full ( ?, e) range [0, 9] × [0, 1) via the ?-index theory of symplectic paths for ? belonging to the unit circle of the complex plane, and the theory of linear operators. After establishing the ?-index decreasing property of the solutions in ? for fixed , we prove the existence of three curves located from left to right in the rectangle [0, 9] × [0, 1), among which two are -1 degeneracy curves and the third one is the right envelope curve of the ?-degeneracy curves, and show that the linear stability pattern of such elliptic Lagrangian solutions changes if and only if the parameter ( ?, e) passes through each of these three curves. Interesting symmetries of these curves are also observed. The linear stability of the singular case when the eccentricity e approaches 1 is also analyzed in detail.
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.
NASA Astrophysics Data System (ADS)
Protogeros, Zacharias A. M.; Melott, Adrian L.; Scherrer, Robert J.
1997-09-01
We test tree-level perturbation theory for Gaussian initial conditions with power spectra P(k)~k^n by comparing the probability distribution function (PDF) for the density predicted by the local Lagrangian approximation (LLA) with the results of numerical gravitational clustering simulations. Our results indicate that our approximation correctly reproduces the evolved density PDF for n=-1 and -2 power spectra up to the weakly non-linear regime, while it shows marginal agreement for power indices n=0 and +1 in the linear regime and poor agreement beyond this point. This suggests that tree-level perturbation theory (as realized in the LLA) can accurately predict the density distribution function for n<=-1, but fails for n>=0.
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.
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.
NASA Astrophysics Data System (ADS)
Alles, Alexandre; Buchert, Thomas; Al Roumi, Fosca; Wiegand, Alexander
2015-07-01
The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the first-order trace solutions that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given together with extensions and applications for accessing the nonperturbative regime. We furnish here construction rules to obtain from Newtonian solutions the gravitoelectric class of relativistic solutions, for which we give the complete perturbation and solution schemes at any order of the perturbations. By construction, these schemes generalize the complete hierarchy of solutions of the Newtonian Lagrangian perturbation theory.
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
Higher Derivative BLG: Lagrangian and Supersymmetry Transformations
Paul Richmond
2012-07-05
Working to lowest non-trivial order in fermions, we consider the four-derivative order corrected Lagrangian and supersymmetry transformations of the Euclidean Bagger-Lambert-Gustavsson theory. By demonstrating supersymmetric invariance of the Lagrangian we determine all numerical coefficients in the system. In addition, the supersymmetry algebra is shown to close on the scalar and gauge fields. We also comment on the extension to Lorentzian and other non-Euclidean $\\mathcal{N}=8$ 3-algebra theories.
Higher Derivative BLG: Lagrangian and Supersymmetry Transformations
Richmond, Paul
2012-01-01
Working to lowest non-trivial order in fermions, we consider the four-derivative order corrected Lagrangian and supersymmetry transformations of the Euclidean Bagger-Lambert-Gustavsson theory. By demonstrating supersymmetric invariance of the Lagrangian we determine all numerical coefficients in the system. In addition, the supersymmetry algebra is shown to close on the scalar and gauge fields. We also comment on the extension to Lorentzian and other non-Euclidean $\\mathcal{N}=8$ 3-algebra theories.
Green function identities in Euclidean quantum field theory
G. Sardanashvily
2006-04-01
Given a generic Lagrangian system of even and odd fields, we show that any infinitesimal transformation of its classical Lagrangian yields the identities which Euclidean Green functions of quantum fields satisfy.
Reverse engineering quantum field theory
NASA Astrophysics Data System (ADS)
Oeckl, Robert
2012-12-01
An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.
Magnetic charges in local field theory
Bernard de Wit; Henning Samtleben; Mario Trigiante
2005-11-16
Novel Lagrangians are discussed in which (non-abelian) electric and magnetic gauge fields appear on a par. To ensure that these Lagrangians describe the correct number of degrees of freedom, tensor gauge fields are included with corresponding gauge symmetries. Non-abelian gauge symmetries that involve both the electric and the magnetic gauge fields can then be realized at the level of a single gauge invariant Lagrangian, without the need of performing duality transformations prior to introducing the gauge couplings. The approach adopted, which was initially developed for gaugings of maximal supergravity, is particularly suited for the study of flux compactifications.
Towards a double field theory on para-Hermitian manifolds
Vaisman, Izu [Department of Mathematics, University of Haifa, Haifa (Israel)] [Department of Mathematics, University of Haifa, Haifa (Israel)
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.
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.
Geometries from field theories
Sinya Aoki; Kengo Kikuchi; Tetsuya Onogi
2015-08-18
We propose a method to define a $d+1$ dimensional geometry from a $d$ dimensional quantum field theory in the $1/N$ expansion. We first construct a $d+1$ dimensional field theory from the $d$ dimensional one via the gradient flow equation, whose flow time $t$ represents the energy scale of the system such that $t\\rightarrow 0$ corresponds to the ultra-violet (UV) while $t\\rightarrow\\infty$ to the infra-red (IR). We then define the induced metric from $d+1$ dimensional field operators. We show that the metric defined in this way becomes classical in the large $N$ limit, in a sense that quantum fluctuations of the metric are suppressed as $1/N$ due to the large $N$ factorization property. As a concrete example, we apply our method to the O(N) non-linear $\\sigma$ model in two dimensions. We calculate the three dimensional induced metric, which is shown to describe an AdS space in the massless limit. We finally discuss several open issues in future studies.
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 ?. 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 ? 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: ?, ?, , and ?, ?, , (in which ? is entropy density and is heat vector) are explored based on conservation and balance laws. It is shown that the choice of ?, ?, , is essential when the entropy inequality is expressed in terms of ?. 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, ? and are considered as arguments of ?, ?, and . When is substituted in the entropy inequality, the resulting conditions eliminate ? 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 ? and those presented in Surana et al. (Acta Mech 224(11):2785—2816, 2013), that are derived using Helmholtz free energy density ?.
Lagrangian model for the evolution of turbulent magnetic and passive scalar fields
NASA Astrophysics Data System (ADS)
Hater, T.; Homann, H.; Grauer, R.
2011-01-01
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.PRLTAO0031-900710.1103/PhysRevLett.97.174501 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.
Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field
Yuri N. Obukhov; Tomas Ramos; Guillermo F. Rubilar
2012-09-13
We develop a relativistic variational model for a nematic liquid crystal interacting with an electro- magnetic field. The constitutive relation for a general anisotropic uniaxial diamagnetic and dielectric medium is analyzed. We discuss light wave propagation in this moving uniaxial medium, for which the corresponding optical metrics are identified explicitly. A Lagrangian for the coupled system of a nematic liquid crystal and the electromagnetic field is constructed, from which a complete set of equations of motion for the system is derived. The canonical energy-momentum and spin tensors are systematically obtained. We compare our results with those within the non-relativistic models. As an application of our general formalism, we discuss the so-called Abraham-Minkowski controversy on the momentum of light in a medium.
Polymer Parametrised Field Theory
Alok Laddha; Madhavan Varadarajan
2008-05-02
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 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 algebra of conformal isometries as well as that of spacetime diffeomorphisms are represented in an anomaly free manner. Semiclassical states can be analysed at the gauge invariant level. It is shown that `physical weaves' necessarily underly 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.
Velasco, E.S.
1986-01-01
This dissertation deals with several topics of field theory. Chapter I is a brief outline of the work presented in the next chapters. In chapter II, the Gauss-Bonnet-Chern theorem for manifolds with boundary is computed using the path integral representation of the Witten index for supersymmetric quantum mechanical systems. In chapter III the action of N = 2 (Poincare) supergravity is obtained in terms of N = 1 superfields. In chapter IV, N = 2 supergravity coupled to the (abelian) vector multiplet is projected into N - 1 superspace. There, the resulting set of constraints is solved in terms of unconstrained prepotential and the action in terms of N = 1 superfields is constructed. In chapter V the set of constraints for N = 2 conformal supergravity is projected into N = 1 superspace and solved in terms of N = 1 conformal supergravity fields a d matter prepotentials. In chapter VI the role of magnetic monopoles in the phase structure of the change one fixed length abelian Higgs model ins the latticer is investigated using analytic and numerical methods. The technique of monopole suppression is used to determine the phase transition lines that are monopole driven. Finally in chapter VII, the role of the charge of the Higgs field in the abelian Higgs model in the lattice is investigated.
Dynamics of Perturbations in Double Field Theory and Non-Relativistic String Theory
Ko, Sung Moon; Meyer, Rene; Park, Jeong-Hyuck
2015-01-01
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 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 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 differentia...
Quantum Field Theory of Fluids
NASA Astrophysics Data System (ADS)
Gripaios, Ben; Sutherland, Dave
2015-02-01
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.
Perturbative Quantum Field Theory via Vertex Algebras
Stefan Hollands; Heiner Olbermann
2009-06-29
In this paper, we explain how perturbative quantum field theory can be formulated in terms of (a version of) vertex algebras. Our starting point is the Wilson-Zimmermann operator product expansion (OPE). Following ideas of a previous paper [arXiv:0802.2198], we consider a consistency (essentially associativity) condition satisfied by the coefficients in this expansion. We observe that the information in the OPE coefficients can be repackaged straightforwardly into "vertex operators" and that the consistency condition then has essentially the same form as the key condition in the theory of vertex algebras. We develop a general theory of perturbations of the algebras that we encounter, similar in nature to the Hochschild cohomology describing the deformation theory of ordinary algebras. The main part of the paper is devoted to the question how one can calculate the perturbations corresponding to a given interaction Lagrangian (such as $\\lambda \\varphi^4$) in practice, using the consistency condition and the corresponding non-linear field equation. We derive graphical rules, which display the vertex operators (i.e., OPE coefficients) in terms of certain multiple series of hypergeometric type.
Perturbative quantum field theory via vertex algebras
NASA Astrophysics Data System (ADS)
Hollands, Stefan; Olbermann, Heiner
2009-11-01
In this paper, we explain how perturbative quantum field theory can be formulated in terms of (a version of) vertex algebras. Our starting point is the Wilson-Zimmermann operator product expansion (OPE). Following ideas of a previous paper (S. Hollands, e-print arXiv:0802.2198), we consider a consistency (essentially associativity) condition satisfied by the coefficients in this expansion. We observe that the information in the OPE coefficients can be repackaged straightforwardly into "vertex operators" and that the consistency condition then has essentially the same form as the key condition in the theory of vertex algebras. We develop a general theory of perturbations of the algebras that we encounter, similar in nature to the Hochschild cohomology describing the deformation theory of ordinary algebras. The main part of the paper is devoted to the question how one can calculate the perturbations corresponding to a given interaction Lagrangian (such as ??4) in practice, using the consistency condition and the corresponding nonlinear field equation. We derive graphical rules, which display the vertex operators (i.e., OPE coefficients) in terms of certain multiple series of hypergeometric type.
Gravitational radiation in d>4 from effective field theory
Cardoso, Vitor [CENTRA, Department de Fisica, Instituto Superior Tecnico, Avenue Rovisco Pais 1, 1049-001 Lisboa (Portugal); Department of Physics and Astronomy, The University of Mississippi, University, Mississippi 38677-1848 (United States); Dias, Oscar J. C. [Departament de Fisica Fonamental, Universitat de Barcelona, Avenue Diagonal 647, E-08028 Barcelona (Spain); Department de Fisica e Centro de Fisica do Porto, Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169 - 007 Porto (Portugal); Figueras, Pau [Center for Particle Theory and Department of Mathematical Sciences, University of Durham, Science Laboratories, South Road, Durham DH1 3LE (United Kingdom)
2008-11-15
Some years ago, a new powerful technique, known as the classical effective field theory, was proposed to describe classical phenomena in gravitational systems. Here we show how this approach can be useful to investigate theoretically important issues, such as gravitational radiation in any spacetime dimension. In particular, we derive for the first time the Einstein-Infeld-Hoffman Lagrangian and we compute Einstein's quadrupole formula for any number of flat spacetime dimensions.
Field Theory of Tachyon Matter
Ashoke Sen
2002-01-01
We propose a field theory for describing the tachyon on a brane-antibrane system near the minimum of the potential. This field theory realizes two known properties of the tachyon effective action: (a) absence of plane-wave solutions around the minimum, and (b) exponential fall off of the pressure at late time as the tachyon field evolves from any spatially homogeneous initial
Gravitational radiative corrections from effective field theory
Goldberger, Walter D
2009-01-01
In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures "post-Minkowskian" corrections to the multipole expansion due to non-linear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corr...
New Terms for the Compact Form of Electroweak Chiral Lagrangian
Zhang, Hong-Hao; Parry, J K; Li, Xue-Song
2007-01-01
The compact form of the electroweak chiral Lagrangian is a reformulation of its original form and is expressed in terms of chiral rotated electroweak gauge fields, which is crucial for relating the information of underlying theories to the coefficients of the low-energy effective Lagrangian. However the compact form obtained in previous works is not complete. In this letter we add several new chiral invariant terms to it and discuss the contributions of these terms to the original electroweak chiral Lagrangian.
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 ?(x(vector sign),t), a new field ?(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field ?(x(vector sign),t), which is defined by means of an additional equation, becomes ?{sup *}(x(vector sign),t) only when q? 1. The solutions for the fields ?(x(vector sign),t) and ?(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.
Steven Weinberg
1995-01-01
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
Scalar field theory on noncommutative Snyder spacetime
Battisti, Marco Valerio [Centre de Physique Theorique, Case 907 Luminy, 13288 Marseille (France); Meljanac, Stjepan [Rudjer Boskovic Institute, Bijenicka c.54, HR-10002 Zagreb (Croatia)
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.
Adaptive time stepping algorithm for Lagrangian transport models: Theory and idealised test cases
NASA Astrophysics Data System (ADS)
Shah, Syed Hyder Ali Muttaqi; Heemink, Arnold Willem; Gräwe, Ulf; Deleersnijder, Eric
2013-08-01
Random walk simulations have an excellent potential in marine and oceanic modelling. This is essentially due to their relative simplicity and their ability to represent advective transport without being plagued by the deficiencies of the Eulerian methods. The physical and mathematical foundations of random walk modelling of turbulent diffusion have become solid over the years. Random walk models rest on the theory of stochastic differential equations. Unfortunately, the latter and the related numerical aspects have not attracted much attention in the oceanic modelling community. The main goal of this paper is to help bridge the gap by developing an efficient adaptive time stepping algorithm for random walk models. Its performance is examined on two idealised test cases of turbulent dispersion; (i) pycnocline crossing and (ii) non-flat isopycnal diffusion, which are inspired by shallow-sea dynamics and large-scale ocean transport processes, respectively. The numerical results of the adaptive time stepping algorithm are compared with the fixed-time increment Milstein scheme, showing that the adaptive time stepping algorithm for Lagrangian random walk models is more efficient than its fixed step-size counterpart without any loss in accuracy.
Currents and the energy-momentum tensor in classical field theory: a fresh look at an old problem
Forger, Frank Michael
Currents and the energy-momentum tensor in classical field theory: a fresh look at an old problem of various methods to define currents and the energy-mo- mentum tensor in classical field theory-known expressions for the current as the variational derivative of the matter field Lagrangian with respect
Modern Classical Electrodynamics and Electromagnetic Radiation - Vacuum Field Theory Aspects
N. N. Bogolubov; A. K. Prykarpatsky
2013-02-16
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and related with them physical aspects. Based on the vacuum field theory no-geometry approach, developed in \\cite{BPT,BPT1}, the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are devised. A problem closely related to the radiation reaction force is analyzed aiming to explain the Wheeler and Feynman reaction radiation mechanism, well known as the absorption radiation theory, and strongly dependent on the Mach type interaction of a charged point particle in an ambient vacuum electromagnetic medium. There are discussed some relationships between this problem and the one derived within the context of the vacuum field theory approach. The R. \\ Feynman's \\textquotedblleft heretical\\textquotedblright\\ approach \\cite{Dy1,Dy2} to deriving the Lorentz force based Maxwell electromagnetic equations is also revisited, its complete legacy is argued both by means of the geometric considerations and its deep relation with the vacuum field theory approach devised before in \\cite{BPT0,BPT1}. \\ Being completely classical, we reanalyze the Feynman's derivation from the classical Lagrangian and Hamiltonian points of view \\ and construct its nontrivial \\ relativistic generalization compatible with the mentioned above vacuum field theory approach.
The Supersymmetry Soft-breaking Lagrangian - Where Experiment and String Theory Meet
Gordon L. Kane
2000-08-29
After an introduction recalling that we expect low energy supersymmetry to be part of our description of nature because of considerable indirect evidence and successful predictions, and a discussion of the essential role of data for formulating and testing string theory, these lectures focus on the role of the supersymmetry soft-breaking Lagrangian in connecting experiment and string theory. How to measure tan$\\beta$ and the soft parameters is examined via a number of applications, and the difficulty of measuring tan$\\beta$ at hadron colliders is explained. In each case the important role of soft phases is made explicit, and the true number of parameters is counted. Applications include the chargino and neutralino sectors, the Higgs sector and how its results change when phases are included, measuring the (relative) gluino phase, CP violation in K and B systems and whether all CP violation can be due to soft phases, how to learn if the LSP is the cold dark matter of the universe, and baryogenesis. It is emphasized that the success of supersymmetry in explaining the breaking of electroweak symmetry is probably its most important achievement, and implications of that explanation for superpartner masses are shown. Combining many of these considerations, a further application argues that a lepton collider of total energy 600 GeV with a polarized beam is one we can be confident will do important physics even after LHC. The question of the origins of CP violation, whether the CKM phase can be zero, and the possibility that the soft phases can tell us about compactification and supersymmetry breaking are discussed. Some of the applications and issues are examined in a D-brane based model that can describe the usual collider and dark matter phenomenology, and includes phases and CP violation as well.
Quantum Field Theory Frank Wilczeky
Wilczek, Frank
Quantum Field Theory Frank Wilczeky Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt achieved and prospective. Possible limitations of quantum eld theory are viewed in the light of its history
Gerbes and quantum field theory
Jouko Mickelsson
2006-03-11
The basic mechanism how gerbes arise in quantum field theory is explained; in particular the case of chiral fermions in background fields is treated. The role of of various gauge group extensions (central extensions of loop groups and their generalizations) is also explained, in relation to index theory computation of the Dixmier-Douady class of a gerbe.
Remarks on noncommutative field theories
M. Gomes
2004-01-01
Some of the motivations and basic properties of noncommutative field models are presented. I also comment on recent developments in the understanding of these peculiar and intriguing theories. A basic problem, which has accompanied the develop- ment of quantum field theory since its inception to our days, concerns the ultraviolet divergences of the perturbative cal- culations. Already in the thirties,
Reconstruction of vector fields for semi-Lagrangian advection on unstructured, staggered grids
Fringer, Oliver B.
to as ``trajectory'' schemes) for coastal ocean models. Most applications of the semi-Lagrangian method use large at the trajectory end points. The original semi-Lagrangian method (Robert, 1981, 1982) evaluates the remaining terms. Wang a, , G. Zhao b , O.B. Fringer a a Environmental Fluid Mechanics Laboratory, Department of Civil
Field Theory of Tachyon Matter
Ashoke Sen
2002-05-02
We propose a field theory for describing the tachyon on a brane-antibrane system near the minimum of the potential. This field theory realizes two known properties of the tachyon effective action: 1) absence of plane-wave solutions around the minimum, and 2) exponential fall off of the pressure at late time as the tachyon field evolves from any spatially homogeneous initial configuration towards the minimum of the potential. Classical solutions in this field theory include non-relativistic matter with arbitrary spatial distribution of energy.
Lagrangian Transport Barriers in 3D Unsteady Flows
NASA Astrophysics Data System (ADS)
Blazevski, Daniel; Haller, George
2013-04-01
Transport barriers in 3D flows form the cores of coherent tracer patterns, acting as locally most repelling or most shearing material surfaces. Here we present an extension of the 2D variational theory of Lagrangian Coherent Structures (LCS) to detect such extremum surfaces in 3D temporally aperiodic velocity fields. Shear LCSs obtained in this fashion provide material boundaries for 3D Lagrangian vortices. We illustrate the theory on model velocity fields.
Pasti, Paolo; Tonin, Mario [Dipartimento di Fisica 'Galileo Galilei', Universita degli Studi di Padova (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via F. Marzolo 8, 35131 Padova (Italy); Samsonov, Igor [Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via F. Marzolo 8, 35131 Padova (Italy); Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk (Russian Federation); Sorokin, Dmitri [Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via F. Marzolo 8, 35131 Padova (Italy)
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.
Strings on pp-waves and massive two dimensional field theories
NASA Astrophysics Data System (ADS)
Maldacena, Juan; Maoz, Liat
2002-12-01
We find a general class of pp-wave solutions of type-IIB string theory such that the light cone gauge worldsheet lagrangian is that of an interacting massive field theory. When the light cone lagrangian has (2,2) supersymmetry we can find backgrounds that lead to arbitrary superpotentials on the worldsheet. We consider situations with both flat and curved transverse spaces. We describe in some detail the background giving rise to the N = 2 sine Gordon theory on the worldsheet. Massive mirror symmetry relates it to the deformed CP1 model (or sausage model) which seems to elude a purely supergravity target space interpretation.
Histories and observables in covariant field theory
NASA Astrophysics Data System (ADS)
Paugam, Frédéric
2011-09-01
Motivated by DeWitt's viewpoint of covariant field theory, we define a general notion of a non-local classical observable that applies to many physical Lagrangian systems (with bosonic and fermionic variables), by using methods that are now standard in algebraic geometry. We review the methods of local functional calculus, as they are presented by Beilinson and Drinfeld, and relate them to our construction. We partially explain the relation of these with Vinogradov's secondary calculus. The methods present here are all necessary to understand mathematically properly, and with simple notions, the full renormalization of the standard model, based on functional integral methods. Our approach is close in spirit to non-perturbative methods since we work with actual functions on spaces of fields, and not only formal power series. This article can be seen as an introduction to well-grounded classical physical mathematics, and as a good starting point to study quantum physical mathematics, which make frequent use of non-local functionals, like for example in the computation of Wilson's effective action. We finish by describing briefly a coordinate-free approach to the classical Batalin-Vilkovisky formalism for general gauge theories, in the language of homotopical geometry.
P. O. Hess; J. C. López Vieyra; C. R. Stephens
1996-11-12
A boson mapping of pair field operators is presented. The mapping preserves all hermiticity properties and the Poisson bracket relations between fields and momenta. The most practical application of the boson mapping is to field theories which exhibit bound states of pairs of fields. As a concrete application we consider, in the low energy limit, the Wick-Cutkosky model with equal mass for the charged fields.
Quantum Field Theory of Fluids
Ben Gripaios; Dave Sutherland
2015-04-23
The quantum theory of fields is largely based on studying perturbations around non-interacting, 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 non-interacting 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 behaviour is radically different to both classical fluids and quantum fields, with interesting physical consequences for fluids in the low temperature regime.
Extended BPH Renormalization of Cutoff Scalar Field Theories
Gordon Chalmers
1994-04-29
We show that general cutoff scalar field theories in four dimensions are perturbatively renormalizable through the use of diagrammatic techniques and an adapted BPH renormalization method. Weinberg's convergence theorem is used to show that operators in the Lagrangian with dimension greater than four, which are divided by powers of the cutoff, produce perturbatively only local divergences in the two-, three-, and four-point correlation functions. We also show that the renormalized Green's functions are the same as in ordinary $\\Phi^4$ theory up to corrections suppressed by inverse powers of the cutoff. These conclusions are consistent with those of existing proofs based on the renormalization group.
A. F. Kord; M. Haddadi Moghaddam; N. Ghasempour
2015-03-10
We investigate some issues on renormalisability of non-anticommutative supersymmetric gauge theory related to field redefinitions. We study one loop corrections to $N=\\frac{1}{2}$ supersymmetric $SU(N)\\times U(1)$ gauge theory coupled to chiral matter in component formalism, and show the procedure which has been introduced for renormalisation is problematic because some terms which are needed for the renormalisability of theory are missed from the Lagrangian. In order to prove the theory is renormalisable, we redefine the gaugino and the auxiliary fields($\\lambda, \\bar F$), which result in a modified form of the Lagrangian in the component formalism. Then, we show the modified Lagrangian has extra terms which are necessary for renormalisability of non-anticommutative supersymmetric gauge field theories. Finally we prove $N = \\frac{1}{2}$ supersymmetric gauge theory is renormalisable up to one loop corrections using standard method of renormalisation; besides, it is shown the effective action is gauge invariant.
Lagrangian self-diffusion of Brownian particles in periodic flow fields
NASA Astrophysics Data System (ADS)
Mauri, Roberto
1995-02-01
The steady transport of Brownian particles convected by a periodic flow field is studied by following the motion of a randomly chosen tagged particle in an otherwise uniform solute concentration field. A nonlocal, Fickian constitutive relation is derived, in which the steady mass flux of Brownian particles equals a convolution integral of the concentration gradient times a (tensorial) diffusion function DL(R). In turn, the diffusion function is uniquely determined via the nth diffusivities, which are determined analytically in terms of the nth cumulants of the probability distribution by exploiting the translational symmetry of the velocity field. The Lagrangian, long-time self-diffusion function DL(R) is shown to be equal to the symmetric part of the Eulerian, gradient diffusion function DE(R). Since the latter characterizes the dissipative steady-state mass transport, while DL(R) describes the fluctuations of the concentration field about its uniform equilibrium value, the equality between DE(R) and DL(R) can be seen as an aspect of the fluctuation-dissipation theorem. Finally, the present results are applied to study the transport of solute particles immersed in a fluid flowing in rectilinear pipes and through periodic fixed beds of spheres at low Péclet number. In the first case, the first six nth diffusivities are determined; in the second, the first two diffusivities are calculated, showing that the enhancement to the second diffusivity due to convection is eight times larger in the direction parallel to the fluid flow than in the transversal direction.
Mathematical Foundations of Field Theory
Luther Rinehart
2015-06-04
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical formulations of field theory suffer greatly from either a failure to explicitly define the field configuration space, or else from the choice to define field operators as distributions. A solution to such problems is given by instead using locally square-integrable functions, and by paying close attention to this space's topology. One benefit of this is a clarification of the field multiplication problem: The pointwise product of fields is still not defined for all states, but it is densely defined, and this is shown to be sufficient for specifying dynamics. Significant progress is also made, through this choice of configuration space, in appropriately representing field states with `infinitely many particles', or those which do not go to zero at infinity.
A systematic approach to the SILH Lagrangian
NASA Astrophysics Data System (ADS)
Buchalla, Gerhard; Catà, Oscar; Krause, Claudius
2015-05-01
We consider the electroweak chiral Lagrangian, including a light scalar boson, in the limit of small ? =v2 /f2. Here v is the electroweak scale and f is the corresponding scale of the new strong dynamics. We show how the conventional SILH Lagrangian, defined as the effective theory of a strongly-interacting light Higgs (SILH) to first order in ?, can be obtained as a limiting case of the complete electroweak chiral Lagrangian. The approach presented here ensures the completeness of the operator basis at the considered order, it clarifies the systematics of the effective Lagrangian, guarantees a consistent and unambiguous power counting, and it shows how the generalization of the effective field theory to higher orders in ? has to be performed. We point out that terms of order ?2, which are usually not included in the SILH Lagrangian, are parametrically larger than terms of order ? / 16?2 that are retained, as long as ? ? 1 / 16?2. Conceptual issues such as custodial symmetry and its breaking are also discussed. For illustration, the minimal composite Higgs model based on the coset SO (5) / SO (4) is considered at next-to-leading order in the chiral expansion. It is shown how the effective Lagrangian for this model is contained as a special case in the electroweak chiral Lagrangian based on SU (2)L ? SU (2)R / SU (2)V.
Thomas Buchert
1993-09-30
The Lagrangian perturbation theory on Friedman-Lemaitre cosmologies investigated and solved up to the second order in earlier papers (Buchert 1992, Buchert \\& Ehlers 1993) is evaluated up to the third order. On its basis a model for non-linear clustering applicable to the modeling of large-scale structure in the Universe for generic initial conditions is formulated. A truncated model is proposed which represents the ``main body'' of the perturbation sequence in the early non-linear regime by neglecting all gravitational sources which describe interaction of the perturbations. However, I also give the irrotational solutions generated by the interaction terms to the third order, which induce vorticity in Lagrangian space. The consequences and applicability of the solutions are put into perspective. In particular, the model presented enables the study of previrialization effects in gravitational clustering and the onset of non-dissipative gravitational turbulence within the cluster environment.
NASA Astrophysics Data System (ADS)
Frishman, Yitzhak; Sonnenschein, Jacob
2014-07-01
Preface; Acknowledgements; Part I. Non-Perturbative Methods in Two Dimensional Field Theory: 1. From massless free scalar field to conformal field theories; 2. Conformal field theory; 3. Theories invariant under affine current algebras; 4. Wess-Zumino-Witten model and Coset models; 5. Solitons and two dimensional integrable models; 6. Bosonization; 7. The large N limit of two dimensional models; Part II. Two Dimensional Non-Perturbative Gauge Dynamics: 8. Gauge theories in two dimensions - basics; 9. Bosonized gauge theories; 10. The t'Hooft solution of 2d QCD; 11. Mesonic spectrum from current algebra; 12. DLCQ and the spectra of QC with fundamental and adjoint fermions; 13. The baryonic spectrum of multiflavour QCD2 in the strong coupling limit; 14. Confinement versus screening; 15. QCD2, Coset models and BRST quantization; 16. Generalized Yang Mills theory on Riemann surface; Part III. From Two to Four Dimensions: 17. Conformal invariance in four dimensional field theories and in QCD; 18. Integrability in four dimensional gauge dynamics; 19. Large N methods in QCD4; 20. From 2d bosonized baryons to 4d skyrmions; 21. From two dimensional solitons to four dimensional magnetic monopoles; 22. Instantons of QCD; 23. Summary, conclusions and outlook; References; Index.
A Superdimensional Dual-covariant Field Theory
Yaroslav Derbenev
2015-08-12
An approach to a Unified Field Theory (UFT) is developed as an attempt to establish unification of the Theory of Quantum Fields (QFT) and General Theory of Relativity (GTR) on the background of a covariant differential calculus. A dual State Vector field (DSV)consisting of covariant and contravariant N-component functions of variables of a N-dimensional unified manifod (UM)is introduced to represents matter. DSV is supposed to transform in a way distinct from that of the differentials of the UM variables. Consequently, the hybrid tensors and a hybrid affine tensor (Dynamic Connection, DC) are introduced. The hybrid curvature form (HCF) is introduced as a covariant derivative of DC. A system of covariant Euler-Lagrange (EL) equations for DSV, DC, and a twin couple of the triadic hybrid tensors (Split Metric, SM)is derived. A scalar Lagrangian form is composed based on a set of principles suited for UFT, including the homogeneity in the UM space, differential irreducibility and scale invariance. The type of the manifold geometry is not specified in advance, in neither local (signature) nor regional (topology) aspects. Equations for DSV play role of the Schroedinger-Dirac equation in space of UM. By the correspondent EL equations, DC and SM are connected to DSV and become responsible for the non-linear features of the system i.e. interactions. In this paper we mark breaking of a background paradigm of the modern QFT, the superposition principle. The issue of the UM-MF dimensionality will be addressed, and relations to the principles and methodology of QFT and GTR will be discussed.
Entropy Viscosity Method for Lagrangian Hydrodynamics and Central Schemes for Mean Field Games
Tomov, Vladimir
2014-04-18
In this dissertation we consider two major subjects. The primary topic is the Entropy Viscosity method for Lagrangian hydrodynamics, the goal of which is to solve numerically the Euler equations of compressible gas dynamics. The second topic...
Scalar Field Theory on Supermanifolds
Mir Hameeda
2012-05-21
In this paper we will analyse a scalar field theory on a spacetime with noncommutative and non-anticommutative coordinates. This will be done using supermanifold formalism. We will also analyse its quantization in path integral formalism.
Holgraphy and BMS field theory
Giovanni Arcioni; Claudio Dappiaggi
2004-09-30
We study the key ingredients of a candidate holographic correspondence in an asymptotically flat spacetimes; in particular we develop the kinematical and the classical dynamical data of a BMS invariant field theory living at null infinity.
Conformal field theory and graphs
V. B. Petkova; J. -B. Zuber
1997-01-21
We review a method of construction of exceptional graphs generalising the ADE Dynkin diagrams which encode the spectrum of conformal field theories described by conformal embeddings of $\\widehat{sl}(n)_k$.
Kwak, Seung Ki
2012-01-01
The existence of momentum and winding modes of closed string on a torus leads to a natural idea that the field theoretical approach of string theory should involve winding type coordinates as well as the usual space-time ...
Double field theory inspired cosmology
Wu, Houwen; Yang, Haitang, E-mail: 2013222020003@stu.scu.edu.cn, E-mail: hyanga@scu.edu.cn [Center for theoretical physics, College of Physical Science and Technology, Sichuan University, Chengdu, 610064 (China)
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.
String field theory and tachyon condensation
Ellwood, Ian Thomas, 1977-
2004-01-01
In this thesis I discuss various aspects of Witten's cubic string field theory. After a brief review of the basics of string field theory we begin by showing how string field theory can be used to check certain conjectures ...
Analytic progress in open string field theory
Kiermaier, Michael Stefan
2009-01-01
Open string field theory provides an action functional for open string fields, and it is thus a manifestly off-shell formulation of open string theory. The solutions to the equation of motion of open string field theory ...
(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.
NASA Astrophysics Data System (ADS)
Sheth, Ravi K.; Chan, Kwan Chuen; Scoccimarro, Román
2013-04-01
Halos are biased tracers of the dark matter distribution. It is often assumed that the initial patches from which halos formed are locally biased with respect to the initial fluctuation field, meaning that the halo-patch fluctuation field can be written as a Taylor series in the dark matter density fluctuation field. If quantities other than the local density influence halo formation, then this Lagrangian bias will generically be nonlocal; the Taylor series must be performed with respect to these other variables as well. We illustrate the effect with Monte Carlo simulations of a model in which halo formation depends on the local shear (the quadrupole of perturbation theory) and provide an analytic model that provides a good description of our results. Our model, which extends the excursion set approach to walks in more than one dimension, works both when steps in the walk are uncorrelated, as well as when there are correlations between steps. For walks with correlated steps, our model includes two distinct types of nonlocality: one is due to the fact that the initial density profile around a patch which is destined to form a halo must fall sufficiently steeply around it—this introduces k dependence to even the linear bias factor, but otherwise only affects the monopole of the clustering signal. The other type of nonlocality is due to the surrounding shear field; this affects the quadratic and higher-order bias factors and introduces an angular dependence to the clustering signal. In both cases, our analysis shows that these nonlocal Lagrangian bias terms can be significant, particularly for massive halos; they must be accounted for in, e.g., analyses of higher-order clustering in Lagrangian or Eulerian space. Comparison of our predictions with measurements of the halo bispectrum in simulations is encouraging. Although we illustrate these effects using halos, our analysis and conclusions also apply to the other constituents of the cosmic web—filaments, sheets and voids.
Tachyonic Field Theory and Neutrino Mass Running
U. D. Jentschura
2012-05-01
In this paper three things are done. (i) We investigate the analogues of Cerenkov radiation for the decay of a superluminal neutrino and calculate the Cerenkov angles for the emission of a photon through a W loop, and for a collinear electron-positron pair, assuming the tachyonic dispersion relation for the superluminal neutrino. The decay rate of a freely propagating neutrino is found to depend on the shape of the assumed dispersion relation, and is found to decrease with decreasing tachyonic mass of the neutrino. (ii) We discuss a few properties of the tachyonic Dirac equation (symmetries and plane-wave solutions), which may be relevant for the description of superluminal neutrinos seen by the OPERA experiment, and discuss the calculation of the tachyonic propagator. (iii) In the absence of a commonly accepted tachyonic field theory, and in view of an apparent "running" of the observed neutrino mass with the energy, we write down a model Lagrangian, which describes a Yukawa-type interaction of a neutrino coupling to a scalar background field via a scalar-minus-pseudoscalar interaction. This constitutes an extension of the standard model. If the interaction is strong, then it leads to a substantial renormalization-group "running" of the neutrino mass and could potentially explain the experimental observations.
Generalization of the Darwin Lagrangian
Frejlak, W.
1988-06-01
Starting from a Lagrangian treatment of classical electrodynamics and using simple heuristic arguments, an effective generalization of the Darwin Lagrangian for point charges moving with arbitrary velocities (v
Quantum field theory without divergences
Altaisky, M. V. [Joint Institute for Nuclear Research, Dubna, 141980 (Russian Federation); and Space Research Institute RAS, Profsoyuznaya 84/32, Moscow, 117997 (Russian Federation)
2010-06-15
It is shown that loop divergences emerging in the Green functions in quantum field theory originate from correspondence of the Green functions to unmeasurable (and hence unphysical) quantities. This is because no physical quantity can be measured in a point, but in a region, the size of which is constrained by the resolution of measuring equipment. The incorporation of the resolution into the definition of quantum fields {phi}(x){yields}{phi}{sup (A)}(x) and appropriate change of Feynman rules results in finite values of the Green functions. The Euclidean {phi}{sup 4}-field theory is taken as an example.
Classical field theory with fermions
NASA Astrophysics Data System (ADS)
Borsányi, Sz.; Hindmarsh, M.
2009-04-01
Classical field theory simulations have been essential for our understanding of non-equilibrium phenomena in particle physics. In this talk we discuss the possible extension of the bosonic classical field theory simulations to include fermions. In principle we use the inhomogeneous mean field approximation as introduced by Aarts and Smit. But in practice we turn from their deterministic technique to a stochastic approach. We represent the fermion field as an ensemble of pairs of spinor fields, dubbed male and female. These c-number fields solve the classical Dirac equation. Our improved algorithm enables the extension of the originally 1+1 dimensional analyses and is suitable for large-scale inhomogeneous settings, like defect networks.
Non-Abelian fractional quantum Hall states and chiral coset conformal field theories
D. C. Cabra; E. Fradkin; G. L. Rossini; F. A. Schaposnik
2000-03-31
We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern-Simons (CS) actions. Our approach exploits the connection between the topological Chern-Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.
Symmetries, sum rules and constraints on effective field theories
NASA Astrophysics Data System (ADS)
Bellazzini, Brando; Martucci, Luca; Torre, Riccardo
2014-09-01
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the scattering amplitudes in the IR to total cross sections integrated all the way up to the UV. Exploiting the group structure of the symmetry, we systematically determine all the independent sum rules and positivity conditions on the expansion coefficients. For effective field theories the amplitudes in the IR are calculable and hence the sum rules set constraints on the parameters of the effective Lagrangian. We clarify the impact of gauging on the sum rules for Goldstone bosons in spontaneously broken gauge theories. We discuss explicit examples that are relevant for WW-scattering, composite Higgs models, and chiral perturbation theory. Certain sum rules based on custodial symmetry and its extensions provide constraints on the Higgs boson coupling to the electroweak gauge bosons.
NASA Astrophysics Data System (ADS)
Berta, Maristella; Bellomo, Lucio; Griffa, Annalisa; Gatimu Magaldi, Marcello; Marmain, Julien; Molcard, Anne; Taillandier, Vincent
2013-04-01
The Lagrangian assimilation algorithm LAVA (LAgrangian Variational Analysis) is customized for coastal areas in the framework of the TOSCA (Tracking Oil Spills & Coastal Awareness network) Project, to improve the response to maritime accidents in the Mediterranean Sea. LAVA assimilates drifters' trajectories in the velocity fields which may come from either coastal radars or numerical models. In the present study, LAVA is applied to the coastal area in front of Toulon (France). Surface currents are available from a WERA radar network (2km spatial resolution, every 20 minutes) and from the GLAZUR model (1/64° spatial resolution, every hour). The cluster of drifters considered is constituted by 7 buoys, transmitting every 15 minutes for a period of 5 days. Three assimilation cases are considered: i) correction of the radar velocity field, ii) correction of the model velocity field and iii) reconstruction of the velocity field from drifters only. It is found that drifters' trajectories compare well with the ones obtained by the radar and the correction to radar velocity field is therefore minimal. Contrarily, observed and numerical trajectories separate rapidly and the correction to the model velocity field is substantial. For the reconstruction from drifters only, the velocity fields obtained are similar to the radar ones, but limited to the neighbor of the drifter paths.
NASA Astrophysics Data System (ADS)
Souvatzis, Petros; Niklasson, Anders M. N.
2013-12-01
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.
Souvatzis, Petros, E-mail: petros.souvatsiz@fysik.uu.se [Department of Physics and Astronomy, Division of Materials Theory, Uppsala University, Box 516, SE-75120, Uppsala (Sweden)] [Department of Physics and Astronomy, Division of Materials Theory, Uppsala University, Box 516, SE-75120, Uppsala (Sweden); Niklasson, Anders M. N., E-mail: amn@lanl.gov [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)] [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
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.
Quantum Theory and Galois Fields
Felix Lev
2006-05-31
We discuss the motivation and main results of a quantum theory over a Galois field (GFQT). The goal of the paper is to describe main ideas of GFQT in a simplest possible way and to give clear and simple arguments that GFQT is a more natural quantum theory than the standard one. The paper has been prepared as a presentation to the ICSSUR' 2005 conference (Besancon, France, May 2-6, 2005).
Yang-Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs effect
E. Cremmer; Sergio Ferrara; L. Girardello; A. van Proeyen
1983-01-01
We derive the lagrangian and transformation laws of the coupled Yang-Mills-matter-supergravity system for unextended n = 1 local supersymmetry. We study the super-Higgs effect and the normal Higgs effect of the Yang-Mills gauge group G. In the case of N chiral multiplets ``minimally'' coupled to supergravity, transforming according to some N-dimensional, generally reducible representation of G, we find a model-independent
Tail terms in gravitational radiation reaction via effective field theory
S. Foffa; R. Sturani
2012-12-24
Gravitational radiation reaction affects the dynamics of gravitationally bound binary systems. Here we focus on the leading "tail" term which modifies binary dynamics at fourth post-Newtonian order, as first computed by Blanchet and Damour. We re-produce this result using effective field theory techniques in the framework of the Lagrangian formalism suitably extended to include dissipation effects. We recover the known logarithmic tail term, consistently with the recent interpretation of the logarithmic tail term in the mass parameter as a renormalization group effect of the Bondi mass of the system.
Gravitational radiative corrections from effective field theory
Walter D. Goldberger; Andreas Ross
2010-07-21
In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures "post-Minkowskian" corrections to the multipole expansion due to non-linear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from non-relativistic binaries, including long distance effects up to 3PN ($v^6$) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.
C. G. Bollini; A. L. De Paoli; M. C. Rocca
2010-02-12
In this paper we show that Ultradistributions of Exponential Type (UET) are appropriate for the description in a consistent way world sheet superstring and superstring field theories. A new Lagrangian for the closed world sheet superstring is obtained. We also show that the superstring field is a linear superposition of UET of compact support (CUET), and give the notion of anti-superstring. We evaluate the propagator for the string field, and calculate the convolution of two of them.
Quantum Field Theory in Graphene
I. V. Fialkovsky; D. V. Vassilevich
2011-11-18
This is a short non-technical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later on, we use this quantity to describe the Quantum Hall Effect, light absorption by graphene, the Faraday effect, and the Casimir interaction.
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 ?-term) and another proportional to its curl (the ? term) assuming certain symmetry conditions are met. Physically, the ?-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.
A unitary and causal effective field theory
Gasparyan, A. M. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt (Germany); SSC RF ITEP, Bolshaya Cheremushkinskaya 25, 117218 Moscow (Russian Federation); Lutz, M. F. M. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt (Germany)
2011-10-24
We report on a novel scheme based on the chiral Lagrangian. It is used to analyze pion-nucleon scattering, pion photoproduction, and nucleon Compton scattering. Subthreshold partial-wave amplitudes are calculated in chiral perturbation theory and analytically extrapolated with constraints imposed by electromagnetic-gauge invariance, causality and unitarity. Experimental quantities are reproduced up to energies {radical}(s){approx_equal}1300 MeV in terms of the parameters relevant at order Q{sup 3}.
Introduction to string theory and conformal field theory
Belavin, A. A., E-mail: belavin@itp.ac.ru; Tarnopolsky, G. M., E-mail: Hetzif@yandex.r [Russian Academy of Sciences, Landau Institute for Theoretical Physics (Russian Federation)
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.
Variational methods for field theories
NASA Astrophysics Data System (ADS)
Ben-Menahem, Shahar
1986-09-01
The thesis is presented in four parts dealing with field theory models: 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. 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 model (Born Oppenheimer approximation). For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. In the 4th part, 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.
Extended BPH renormalization of cutoff scalar field theories
Chalmers, G.
1996-06-01
We show through the use of diagrammatic techniques and a newly adapted BPH renormalization method that general momentum cutoff scalar field theories in four dimensions are perturbatively renormalizable. Weinberg{close_quote}s convergence theorem is used to show that operators in the Lagrangian with dimension greater than four, which are divided by powers of the cutoff, produce perturbatively only local divergences in the two-, three-, and four-point correlation functions. The naive use of the convergence theorem together with the BPH method is not appropriate for understanding the local divergences and renormalizability of these theories. We also show that the renormalized Green{close_quote}s functions are the same as in ordinary {Phi}{sup 4} theory up to corrections suppressed by inverse powers of the cutoff. These conclusions are consistent with those of existing proofs based on the renormalization group. {copyright} {ital 1996 The American Physical Society.}
Extended BPH renormalization of cutoff scalar field theories
NASA Astrophysics Data System (ADS)
Chalmers, Gordon
1996-06-01
We show through the use of diagrammatic techniques and a newly adapted BPH renormalization method that general momentum cutoff scalar field theories in four dimensions are perturbatively renormalizable. Weinberg's convergence theorem is used to show that operators in the Lagrangian with dimension greater than four, which are divided by powers of the cutoff, produce perturbatively only local divergences in the two-, three-, and four-point correlation functions. The naive use of the convergence theorem together with the BPH method is not appropriate for understanding the local divergences and renormalizability of these theories. We also show that the renormalized Green's functions are the same as in ordinary ?4 theory up to corrections suppressed by inverse powers of the cutoff. These conclusions are consistent with those of existing proofs based on the renormalization group.
Electromagnetic form factors of the nucleon in effective field theory
T. Bauer; J. C. Bernauer; S. Scherer
2012-09-18
We calculate the electromagnetic form factors of the nucleon to third chiral order in manifestly Lorentz-invariant effective field theory. The rho and omega mesons as well as the Delta(1232) resonance are included as explicit dynamical degrees of freedom. To obtain a self-consistent theory with respect to constraints we consider the proper relations among the couplings of the effective Lagrangian. For the purpose of generating a systematic power counting, the extended on-mass-shell renormalization scheme is applied in combination with the small-scale expansion. The results for the electric and magnetic Sachs form factors are analyzed in terms of experimental data and compared to previous findings in the framework of chiral perturbation theory. The pion-mass dependence of the form factors is briefly discussed.
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.
NASA Astrophysics Data System (ADS)
Barutello, Vivina; Jadanza, Riccardo D.; Portaluri, Alessandro
2015-07-01
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 ? 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: ?-homogeneous potentials, for ? 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 ? and the mass parameter ?, 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.
Quantum Algorithms for Quantum Field Theories
Preskill, John
Quantum Algorithms for Quantum Field Theories Stephen P. Jordan,1 * Keith S. M. Lee,2 John Preskill3 Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role probabilities in a massive quantum field theory with quartic self-interactions (f4 theory) in spacetime of four
A multisymplectic approach to defects in integrable classical field theory
V. Caudrelier; A. Kundu
2015-02-20
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 Schr\\"odinger (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 B\\"acklund 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.
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 [Triangle de la Physique, CPHT Ecole Polytechnique, IPhT Saclay, LPT Orsay and Laboratoire de Physique Theorique, CNRS UMR 8627, Universite Paris XI, F-91405 Orsay Cedex (France); Girelli, Florian [School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia); Oriti, Daniele [Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Muehlenberg 1, 14467 Golm (Germany)
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 and Non-Relativistic String Theory
Sung Moon Ko; Charles Melby-Thompson; Rene Meyer; Jeong-Hyuck Park
2015-08-05
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 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 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 Schr\\"odinger conformal symmetry.
Recombination of Intersecting D-branes in Tachyon Field Theory
Wung-Hong Huang
2003-05-13
The mechanism of recombination of intersecting D-branes is investigated within the framework of effective tachyon field theory. We regard the branes as the kink-type tachyon condensed states and use the effective two-tachyon Lagrangian to study the off-diagonal fluctuations therein. It is seen that there is a tachyonic mode in the off-diagonal fluctuations, which signs the instability of the intersecting D-branes. We diagonalize the two-by-two tachyonic matrix field and see that the corresponding eigenfunctions could be used to describe the new recombined branes. Our prescription can be extended to discuss the general behavior of the recombination of intersection D-branes with arbitrary shapes. We present in detail the physical reasons behind the mathematical process of diagonalizing the tachyonic matrix field.
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.
Rearranging pionless effective field theory
NASA Astrophysics Data System (ADS)
Beane, Silas R.; Savage, Martin J.
2001-11-01
We point out a redundancy in the operator structure of the pionless effective field theory, EFT(??), 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, np?d ?, and Compton scattering from the deuteron. Unlike EFT(??), the 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.
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.
Gravity Duals for Nonrelativistic Conformal Field Theories
McGreevy, John
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 ...
Effective Field Theory in Nuclear Physics
Martin J. Savage
2000-07-11
I review recent developments in the application of effective field theory to nuclear physics. Emphasis is placed on precision two-body calculations and efforts to formulate the nuclear shell model in terms of an effective field theory.
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.
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.
Effective-Lagrangian approach to the theory of pion photoproduction in the. Delta. (1232) region
Davidson, R.M.; Mukhopadhyay, N.C.; Wittman, R.S. )
1991-01-01
We investigate theoretical uncertainties and model dependence in the extraction of the nucleon-{Delta}(1232) electromagnetic transition amplitudes from the multipole data base. Our starting point is an effective Lagrangian incorporating chiral symmetry, which includes, at the tree level, the pseudovector nucleon Born terms, leading {ital t}-channel vector-meson exchanges, and {ital s}- and {ital u}-channel {Delta} exchanges. We express the nucleon-{Delta} transition magnetic dipole ({ital M}1) and electric quadrupole ({ital E}2) amplitudes in terms of two independent gauge couplings at the {gamma}{ital N}{Delta} vertex, and fit these to various multipole data sets. We find a large sensitivity to the method used in unitarizing the amplitude, and extract the {ital E}2/{ital M}1 ratio (EMR) to be {ital negative}, with a magnitude of around 1.5%. The resonant amplitudes in this work are of interest to the test of topical hadron models inspired by QCD: the sign of the EMR, extracted by us, is in accord with that predicted by most realistic models, and its magnitude lies between the predictions of the quark shell model and the Skyrmion model. Finally, our work provides a phenomenologically satisfying unitary amplitude for pion photoproduction off nucleons, which can be used as a realistic starting point for theoretical studies of this process in complex nuclei.
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 of Interacting Tachyons
J. Dhar; E. C. G. Sudarshan
1968-01-01
A quantum field theory of spin-0 particles traveling with speeds greater than that of light has been constructed. The theory constructed here is explicitly Lorentz-invariant; and the quanta of the field obey Bose statistics. Formalism developed for the free field has been extended to the case of interaction of these particles with nucleons. A new feature of theory is the
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.
Fractional Statistics in Algebraic Quantum Field Theory
van Elburg, Ronald A.J.
Fractional Statistics in Algebraic Quantum Field Theory and the Fractional Quantum Hall-states . . . . . . . . . . . . . . . . . . . . . . 28 3 Effective Gauge Theory for Quantum Hall-Effects 33 3.1 Effective Gauge Field Action the connection of the Fractional Quantum Hall Effect with Braid statistics in Algebraic Quantum Field Theory
Vertex operator algebras and conformal field theory
Huang, Y.Z. )
1992-04-20
This paper discusses conformal field theory, an important physical theory, describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. The study of conformal field theory will deepen the understanding of these theories and will help to understand string theory conceptually. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and Lie groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera and elliptic cohomology, Calabi-Yau manifolds, tensor categories, and knot theory, are revealed in the study of conformal field theory. It is therefore believed that the study of the mathematics involved in conformal field theory will ultimately lead to new mathematical structures which would be important to both mathematics and physics.
NASA Astrophysics Data System (ADS)
Vollhardt, Dieter; Byczuk, Krzysztof; Kollar, Marcus
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.
Chiral Symmetry Restoration in Effective Lagrangian Models
NASA Astrophysics Data System (ADS)
Weiss, Christian J.
We study the restoration of chiral symmetry in dense baryon matter using effective lagrangian models of QCD, in which baryons are described as topological solitons. Starting from the breaking of scale invariance and chiral symmetry in the QCD vacuum, we discuss the foundations of effective lagrangians and their relevance for applications to dense matter. Soliton models, such as the Skyrme model, show a phase transition at high densities, whose order parameter is the average scalar field. We investigate the properties of the two phases of the effective theory and show that the phase transition corresponds to the restoration of the chiral symmetry of QCD. We argue that it should not be understood as deconfinement. We then consider this phase transition in the context of the Cheshire Cat principle, which provides the link to the underlying quarks of QCD. An analogue of the Cheshire Cat property of the chiral bag model for baryons is found in solitons of effective lagrangians with a scalar glueball field. The Cheshire Cat interpretation of the results of effective lagrangians provides a consistent picture of chiral symmetry restoration at high densities. To verify this interpretation explicitly, we finally generalize the effective lagrangian approach to dense matter to a chiral bag model description with quark degrees of freedom.
Hamiltonian Anomalies from Extended Field Theories
NASA Astrophysics Data System (ADS)
Monnier, Samuel
2015-09-01
We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.
A Student's Guide to Lagrangians and Hamiltonians
NASA Astrophysics Data System (ADS)
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
Classical Theorems in Noncommutative Quantum Field Theory
M. Chaichian; M. Mnatsakanova; A. Tureanu; Yu. Vernov
2006-12-12
Classical results of the axiomatic quantum field theory - Reeh and Schlieder's theorems, irreducibility of the set of field operators and generalized Haag's theorem are proven in SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory. In SO(1,3) invariant theory new consequences of generalized Haag's theorem are obtained. It has been proven that the equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and thus the total cross-sections in these theories.
Zacharias A. M. Protogeros; Robert J. Scherrer
1996-03-28
We examine local Lagrangian approximations for the gravitational evolution of the density distribution function. In these approximations, the final density at a Lagrangian point q at a time t is taken to be a function only of t and of the initial density at the same Lagrangian point. A general expression is given for the evolved density distribution function for such approximations, and we show that the vertex generating function for a local Lagrangian mapping applied to an initially Gaussian density field bears a simple relation to the mapping itself. Using this result, we design a local Lagrangian mapping which reproduces nearly exactly the hierarchical amplitudes given by perturbation theory for gravitational evolution. When extended to smoothed density fields and applied to Gaussian initial conditions, this mapping produces a final density distribution function in excellent agreement with full numerical simulations of gravitational clustering. We also examine the application of these local Lagrangian approximations to non-Gaussian initial conditions.
Aging Logarithmic Galilean Field Theories
Seungjoon Hyun; Jaehoon Jeong; Bom Soo Kim
2013-06-13
We analytically compute correlation and response functions of scalar operators for the systems with Galilean and corresponding aging symmetries for general spatial dimensions $d$ and dynamical exponent $z$, along with their logarithmic and logarithmic squared extensions, using the gauge/gravity duality. These non-conformal extensions of the aging geometry are marked by two dimensionful parameters, eigenvalue $\\mathcal M$ of an internal coordinate and aging parameter $\\alpha$. We further perform systematic investigations on two-time response functions for general $d$ and $z$, and identify the growth exponent as a function of the scaling dimensions $\\Delta$ of the dual field theory operators and aging parameter $\\alpha$ in our theory. The initial growth exponent is only controlled by $\\Delta$, while its late time behavior by $\\alpha$ as well as $\\Delta$. These behaviors are separated by a time scale order of the waiting time. We attempt to make contact our results with some field theoretical growth models, such as Kim-Kosterlitz model at higher number of spatial dimensions $d$.
A Naturally Renormalized Quantum Field Theory
S. Rouhani; M. V. Takook
2006-07-07
It was shown that quantum metric fluctuations smear out the singularities of Green's functions on the light cone [1], but it does not remove other ultraviolet divergences of quantum field theory. We have proved that the quantum field theory in Krein space, {\\it i.e.} indefinite metric quantization, removes all divergences of quantum field theory with exception of the light cone singularity [2,3]. In this paper, it is discussed that the combination of quantum field theory in Krein space together with consideration of quantum metric fluctuations, results in quantum field theory without any divergences.
Large N Field Theories, String Theory and Gravity
NASA Astrophysics Data System (ADS)
Maldacena, Juan
2006-08-01
We describe the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the {N} = 4 supersymmetric gauge theory in four dimensions.
Large N Field Theories, String Theory and Gravity
NASA Astrophysics Data System (ADS)
Maldacena, Juan
2001-04-01
We describe the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the {N} = 4 supersymmetric gauge theory in four dimensions.
M. Amabili
2003-01-01
Large-amplitude (geometrically non-linear) vibrations of circular cylindrical shells subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated. The Lagrange equations of motion are obtained by an energy approach, retaining damping through Rayleigh's dissipation function. Four different non-linear thin shell theories, namely Donnell's, Sanders–Koiter, Flügge–Lur’e-Byrne and Novozhilov's theories, which neglect rotary inertia and shear deformation,
Gauge fields and fermions in tachyon effective field theories
Joseph A. Minahan; Barton Zwiebach
2001-01-01
In this paper we incorporate gauge fields into the tachyon field theory models for unstable D-branes in bosonic and in type-II string theories. The chosen couplings yield massless gauge fields and an infinite set of equally spaced massive gauge fields on codimension one branes. A lack of a continuum spectrum is taken as evidence that the stable tachyon vacuum does
Mathematical quantization of Hamiltonian field theories
Stoyanovsky, A V
2015-01-01
We define the renormalized evolution operator of the Schr\\"odinger equation in the infinite dimensional Weyl-Moyal algebra during a time interval for a wide class of Hamiltonians depending on time. This leads to a mathematical definition of quantum field theory $S$-matrix and Green functions. We show that for renormalizable field theories, our theory yields the renormalized perturbation series of perturbative quantum field theory. All the results are based on the Feynman graph series technique.
Topics in Effective Field Theory for Lattice QCD
Andre Walker-Loud
2006-08-16
In this work, we extend and apply effective field theory techniques to systematically understand a subset of lattice artifacts which pollute the lattice correlation functions for a few processes of physical interest. Where possible, we compare to existing lattice QCD calculations. In particular, we extend the heavy baryon Lagrangian to the next order in partially quenched chiral perturbation theory and use it to compute the masses of the lightest spin-1/2 and spin-3/2 baryons to next-to-next-to leading order. We then construct the twisted mass chiral Lagrangian for baryons and apply it to compute the lattice spacing corrections to the baryon masses simulated with twisted mass lattice QCD. We extend computations of the nucleon electromagnetic structure to account for finite volume effects, as these observables are particularly sensitive to the finite extent of the lattice. We resolve subtle peculiarities for lattice QCD simulations of polarizabilities and we show that using background field techniques, one can make predictions for the 4 spin-dependent nucleon polarizabilities, quantities which are difficult to access experimentally. We then discuss the two-pion system in finite volume, determining the exponentially small volume corrections necessary for lattice determinations of the scattering parameters. We also determine the lattice spacing artifacts that arise for a mixed-action lattice simulation of the two-pion system with Ginsparg-Wilson valence quarks and staggered sea quarks. We show that the isospin 2 scattering length has a near continuum like behavior, differing from the chiral perturbation theory calculation by a computable difference.
Einstein's vierbein field theory of curved space
Jeffrey Yepez
2011-06-10
General Relativity theory is reviewed following the vierbein field theory approach proposed in 1928 by Einstein. It is based on the vierbein field taken as the "square root" of the metric tensor field. Einstein's vierbein theory is a gauge field theory for gravity; the vierbein field playing the role of a gauge field but not exactly like the vector potential field does in Yang-Mills theory--the correction to the derivative (the covariant derivative) is not proportional to the vierbein field as it would be if gravity were strictly a Yang-Mills theory. Einstein discovered the spin connection in terms of the vierbein fields to take the place of the conventional affine connection. To date, one of the most important applications of the vierbein representation is for the derivation of the correction to a 4-spinor quantum field transported in curved space, yielding the correct form of the covariant derivative. Thus, the vierbein field theory is the most natural way to represent a relativistic quantum field theory in curved space. Using the vierbein field theory, presented is a derivation of the the Einstein equation and then the Dirac equation in curved space. Einstein's original 1928 manuscripts translated into English are included.
The electroweak chiral Lagrangian reanalyzed
NASA Astrophysics Data System (ADS)
Nyffeler, Andreas; Schenk, Andreas
2000-12-01
In this paper we reanalyze the electroweak chiral Lagrangian with particular focus on two issues related to gauge invariance. Our analysis is based on a manifestly gauge-invariant approach that we introduced recently. It deals with gauge-invariant Green's functions and provides a method to evaluate the corresponding generating functional without fixing the gauge. First we show, for the case where no fermions are included in the effective Lagrangian, that the set of low-energy constants currently used in the literature is redundant. In particular, by employing the equations of motion for the gauge fields one can choose to remove two low-energy constants which contribute to the self-energies of the gauge bosons. If fermions are included in the effective field theory analysis the situation is more involved. Even in this case, however, these contributions to the self-energies of the gauge bosons can be removed. The relation of this result to the experimentally determined values for the oblique parameters S, T, and U is discussed. In the second part of the paper we consider the matching relation between a full and an effective theory. We show how the low-energy constants of the effective Lagrangian can be determined by matching gauge-invariant Green's functions in both theories. As an application we explicitly evaluate the low-energy constants for the standard model with a heavy Higgs boson. The matching at the one-loop level and at next-to-leading order in the low-energy expansion is performed employing functional methods.
Permutation Orbifolds in Conformal Field Theories and String Theory
M. Maio
2011-11-03
We summarize the results obtained in the last few years about permutation orbifolds in two-dimensional conformal field theories, their application to string theory and their use in the construction of four-dimensional heterotic string models.
Large N field theories, string theory and gravity
Ofer Aharony; Steven S. Gubser; Juan Maldacena; Hirosi Ooguri; Yaron Oz
2000-01-01
We review the holographic correspondence between field theories and string\\/M theory, focusing on the relation between compactifications of string\\/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime
Standard Model Double Field Theory
Choi, Kang-Sin
2015-01-01
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 $\\mathbf{O}(4,4)$ T-duality covariant manner and manifests two independent local Lorentz symmetries, $\\mathbf{Spin}(1,3)\\times\\mathbf{Spin}(3,1)$. 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 $\\theta$-term is no longer allowed by the symmetry, and hence the strong CP problem is solved. There are now stronger constraints imposed on the possible higher order corrections. We urge experimentalists to test if the quarks and the leptons belong to the same spin class or not.
Standard Model Double Field Theory
Kang-Sin Choi; Jeong-Hyuck Park
2015-06-17
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 $\\mathbf{O}(4,4)$ T-duality covariant manner and manifests two independent local Lorentz symmetries, $\\mathbf{Spin}(1,3)\\times\\mathbf{Spin}(3,1)$. 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 $\\theta$-term is no longer allowed by the symmetry, and hence the strong CP problem is solved. There are now stronger constraints imposed on the possible higher order corrections. We urge experimentalists to test if the quarks and the leptons belong to the same spin class or not.
Receptive Field Plasticity Theories of Learning
Blais, Brian
Receptive Field Plasticity Theories of Learning Model of the Mouse Deprivation in Mouse Plasticity Between Physics and Biology web.bryant.edu/bblais/research.html #12;Receptive Field Plasticity Theories basic observations of plasticity in the brain, and present some theories which explain them. Through
Descent Relations in Cubic Superstring Field Theory
Aref'eva, I Ya; 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 and in the NS fermionic string field theory in the kappa and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.
Descent Relations in Cubic Superstring Field Theory
I. Ya. Aref'eva; R. V. Gorbachev; P. B. Medvedev; D. V. Rychkov
2008-01-15
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 and in the NS fermionic string field theory in the kappa and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.
Perturbative nonequilibrium thermal field theory
NASA Astrophysics Data System (ADS)
Millington, Peter; Pilaftsis, Apostolos
2013-10-01
We present a new perturbative formulation of nonequilibrium thermal field theory, based upon nonhomogeneous free propagators and time-dependent vertices. Our approach to nonequilibrium dynamics yields time-dependent diagrammatic perturbation series that are free of pinch singularities, without the need to resort to quasiparticle approximation or effective resummations of finite widths. In our formalism, the avoidance of pinch singularities is a consequence of the consistent inclusion of finite-time effects and the proper consideration of the time of observation. After arriving at a physically meaningful definition of particle number densities, we derive master time evolution equations for statistical distribution functions, which are valid to all orders in perturbation theory. The resulting equations do not rely upon a gradient expansion of Wigner transforms or involve any separation of time scales. To illustrate the key features of our formalism, we study out-of-equilibrium decay dynamics of unstable particles in a simple scalar model. In particular, we show how finite-time effects remove the pinch singularities and lead to violation of energy conservation at early times, giving rise to otherwise kinematically forbidden processes. The non-Markovian nature of the memory effects as predicted in our formalism is explicitly demonstrated.
Dual of the Janus solution: An interface conformal field theory
Clark, A.B.; Karch, A.; Freedman, D.Z.; Schnabl, M.
2005-03-15
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. 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{sup '} which is the fourth descendent of the primary TrX{sup {l_brace}}{sup I}X{sup J{r_brace}} 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 g{sub YM}{sup 2}, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value
Quasiparticles operators in conformal field theories
Cabra, Daniel C. [Departamento de Fisica, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata (Argentina)
1998-01-10
Gauge invariant fermion fields in fermionic coset models play a central role in the quasiparticle description of certain Conformal Field Theories (CFT's). We briefly outline the description for unitary minimal models, and show how spinon fields in SU(N){sub 1} Wess-Zumino-Witten (WZW) theories appear naturally within this scheme.
Einstein's vierbein field theory of curved space
Yepez, Jeffrey
2011-01-01
General Relativity theory is reviewed following the vierbein field theory approach proposed in 1928 by Einstein. It is based on the vierbein field taken as the "square root" of the metric tensor field. Einstein's vierbein theory is a gauge field theory for gravity; the vierbein field playing the role of a gauge field but not exactly like the vector potential field does in Yang-Mills theory--the correction to the derivative (the covariant derivative) is not proportional to the vierbein field as it would be if gravity were strictly a Yang-Mills theory. Einstein discovered the spin connection in terms of the vierbein fields to take the place of the conventional affine connection. To date, one of the most important applications of the vierbein representation is for the derivation of the correction to a 4-spinor quantum field transported in curved space, yielding the correct form of the covariant derivative. Thus, the vierbein field theory is the most natural way to represent a relativistic quantum field theory in...
Noncommutative Tachyons And String Field Theory
Edward Witten
2000-01-01
It has been shown recently that by turning on a large noncommutativity parameter, the description of tachyon condensation in string theory can be drastically simplified. We reconsider these issues from the standpoint of string field theory, showing that, from this point of view, the key fact is that in the limit of a large B-field, the string field algebra factors
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.
Homotopy Classification of Bosonic String Field Theory
Korbinian Muenster; Ivo Sachs
2012-08-28
We prove the decomposition theorem for the loop homotopy algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra we show that string field theory is background independent and locally unique in a very precise sense. Finally we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories.
Homotopy Classification of Bosonic String Field Theory
NASA Astrophysics Data System (ADS)
Münster, Korbinian; Sachs, Ivo
2014-09-01
We prove the decomposition theorem for the loop homotopy Lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra, we show that string field theory is background independent and locally unique in a very precise sense. Finally, we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories.
Fermions and supersymmetry in E6(6) exceptional field theory
NASA Astrophysics Data System (ADS)
Musaev, Edvard T.; Samtleben, Henning
2015-03-01
We construct the supersymmetric completion of E6(6)-covariant exceptional field theory. The theory is based on a (5 + 27)-dimensional generalized space-time subject to a covariant section constraint. The fermions are tensors under the local Lorentz group SO(1, 4) × USp(8) and transform as weighted scalars under the E6(6) (internal) generalized diffeomorphisms. We present the complete Lagrangian and prove its invariance under supersymmetry. Upon explicit solution of the section constraint the theory embeds full D = 11 supergravity and IIB supergravity, respectively.
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.
Non-Abelian gauge field theory in scale relativity
Laurent Nottale; Marie-Noëlle Célérier; Thierry Lehner
2006-05-29
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a non-differentiable 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.
BPHZ renormalization of phi/sup 4/ field theory in curved spacetime
Bunch, T.S.
1981-01-01
A proof is given to all orders in perturbation theory of the renormalizability of phi/sup 4/ field theory in curved spacetime. The proof is based on the BPHZ definition of a renormalized Feynman integrand and uses dimensional regularization to ensure that products of Feynman propagators are well-defined distributions. The explicit structure of the pole terms in the Feynman intergrand is obtained using a local momentum space representation of the Feynman propagator and is shown to be of a form which can be cancelled by counterterms in the scalar field Lagrangian. The proof given is, technically, only valid for metrics which have been analytically continued to Euclidean (+ + + +) signature.
Heating Field Theory the ``Environmentally Friendly'' Way!
M. A. van Ejick; Denjoe O'Connor; C. R. Stephens
1993-10-31
We discuss how to implement an ``environmentally friendly'' renormalization in the context of finite temperature field theory. Environmentally friendly renormalization provides a method for interpolating between the different effective field theories which characterize different asymptotic regimes. We give explicit two loop Pad\\'e resummed results for $\\l\\ff$ theory for $T>T_c$. We examine the implications for non-Abelian gauge theories.
The quantum character of physical fields. Foundations of field theories
L. I. Petrova
2006-03-15
The existing field theories are based on the properties of closed exterior forms, which are invariant ones and correspond to conservation laws for physical fields. Hence, to understand the foundations of field theories and their unity, one has to know how such closed exterior forms are obtained. In the present paper it is shown that closed exterior forms corresponding to field theories are obtained from the equations modelling conservation (balance)laws for material media. It has been developed the evolutionary method that enables one to describe the process of obtaining closed exterior forms. The process of obtaining closed exterior forms discloses the mechanism of evolutionary processes in material media and shows that material media generate, discretely, the physical structures, from which the physical fields are formed. This justifies the quantum character of field theories. On the other hand, this process demonstrates the connection between field theories and the equations for material media and points to the fact that the foundations of field theories must be conditioned by the properties of material media. It is shown that the external and internal symmetries of field theories are conditioned by the degrees of freedom of material media. The classification parameter of physical fields and interactions, that is, the parameter of the unified field theory, is connected with the number of noncommutative balance conservation laws for material media.
Tachyon Condensation: Calculations in String Field Theory
Pieter-Jan De Smet
2001-09-24
In this Ph.D. thesis, we study tachyon condensation in string field theories. In chapter 2, we review Witten's bosonic string field theory and calculate the tachyon potential. In chapter 3, we calculate the tachyon potential in Berkovits' superstring field theory. In chapter 4, we look for exact solutions in a toy model. Unpublished result: we use conservation laws to calculate the level (4,8) approximation of the tachyon potential in Berkovits' superstring field theory. We verify Sen's conjecture up to 94.4%.
Designer gravity and field theory effective potentials.
Hertog, Thomas; Horowitz, Gary T
2005-06-10
Motivated by the anti-de Sitter conformal field theory correspondence, we show that there is remarkable agreement between static supergravity solutions and extrema of a field theory potential. For essentially any function V(alpha) there are boundary conditions in anti-de Sitter space so that gravitational solitons exist precisely at the extrema of V and have masses given by the value of V at these extrema. Based on this, we propose new positive energy conjectures. On the field theory side, each function V can be interpreted as the effective potential for a certain operator in the dual field theory. PMID:16090378
Designer Gravity and Field Theory Effective Potentials
Hertog, Thomas; Horowitz, Gary T. [Department of Physics, UCSB, Santa Barbara, California 93106 (United States)
2005-06-10
Motivated by the anti-de Sitter conformal field theory correspondence, we show that there is remarkable agreement between static supergravity solutions and extrema of a field theory potential. For essentially any function V({alpha}) there are boundary conditions in anti--de Sitter space so that gravitational solitons exist precisely at the extrema of V and have masses given by the value of V at these extrema. Based on this, we propose new positive energy conjectures. On the field theory side, each function V can be interpreted as the effective potential for a certain operator in the dual field theory.
Functional Integration for Quantum Field Theory
J. LaChapelle
2006-10-16
The functional integration scheme for path integrals advanced by Cartier and DeWitt-Morette is extended to the case of fields. The extended scheme is then applied to quantum field theory. Several aspects of the construction are discussed.
The spinor field theory of the photon
Ruo Peng Wang
2011-09-18
I introduce a spinor field theory for the photon. The three-dimensional vector electromagnetic field and the four-dimensional vector potential are components of this spinor photon field. A spinor equation for the photon field is derived from Maxwell's equations,the relations between the electromagnetic field and the four-dimensional vector potential, and the Lorentz gauge condition. The covariant quantization of free photon field is done, and only transverse photons are obtained. The vacuum energy divergence does not occur in this theory. A covariant "positive frequency" condition is introduced for separating the photon field from its complex conjugate in the presence of the electric current and charge.
General Gauge Field Theory And Its Application
Ning Wu
1998-07-19
A gauge field model, which simultaneously has strict local gauge symmetry and contains massive general gauge bosons, is discussed in this paper. The model has SU(N) gauge symmetry. In order to introduce the mass term of gauge fields directly without violating the gauge symmetry of the theory, two sets of gauge fields will be introduced into the theory. After some transformations, one set of gauge fields obtain masses and another set of gauge fields keep massless. In the limit $\\alpha \\longrightarrow 0$ or $\\alpha \\longrightarrow \\infty$, the gauge field model discussed in this paper will return to Yang-Mills gauge field model. Finally, some applications of this model are discussed.
Democratic superstring field theory: gauge fixing
NASA Astrophysics Data System (ADS)
Kroyter, Michael
2011-03-01
We show that a partial gauge fixing of the NS sector of the democratic-picture superstring field theory leads to the non-polynomial theory. Moreover, by partially gauge fixing the Ramond sector we obtain a non-polynomial fully RNS theory at pictures 0 and 1/2 . Within the democratic theory and in the partially gauge fixed theory the equations of motion of both sectors are derived from an action. We also discuss a representation of the non-polynomial theory analogous to a manifestly two-dimensional representation of WZW theory and the action of bosonic pure-gauge solutions. We further demonstrate that one can consistently gauge fix the NS sector of the democratic theory at picture number -1. The resulting theory is new. It is a {mathbb{Z}_2} dual of the modified cubic theory. We construct analytical solutions of this theory and show that they possess the desired properties.
NASA Astrophysics Data System (ADS)
Moayedi, S. K.; Setare, M. R.; Khosropour, B.
2013-11-01
In the 1990s, Kempf and his collaborators Mangano and Mann introduced a D-dimensional (?, ??)-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length (\\triangle Xi)\\min = \\hbar ? {D? +? '}, \\forall i\\in \\{1, 2, ..., D\\}. In this work, the Lagrangian formulation of a magnetostatic field in three spatial dimensions (D = 3) described by Kempf algebra is presented in the special case of ?? = 2? up to the first-order over ?. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee-Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot-Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is 4.42×10-19 m. The relationship between magnetostatics with a minimal length and the Gaete-Spallucci nonlocal magnetostatics [J. Phys. A: Math. Theor. 45, 065401 (2012)] is investigated.
Singularity theory and N = 2 superconformal field theories
Warner, N.P.
1989-01-01
The N = 2 superconformal field theories that appear at the fixed points of the renormalization group flows of Landau-Ginsburg models are discussed. Some of the techniques of singularity theory are employed to deduce properties of these superconformal theories. These ideas are then used to deduce the relationship between Calabi-Yau compactifications and tensored discrete series models. The chiral rings of general N = 2 superconformal theories are also described. 14 refs.
Pascual Jordan's legacy and the ongoing research in quantum field theory?
NASA Astrophysics Data System (ADS)
Schroer, B.
2010-04-01
Pascual Jordan's path-breaking role as the protagonist of quantum field theory (QFT) is recalled and his friendly dispute with Dirac's particle-based relativistic quantum theory is presented as the start of the field-particle conundrum which, though in modified form, persists up to this date. Jordan had an intuitive understanding that the existence of a causal propagation with finite propagation speed in a quantum theory led to radically different physical phenomena than those of QM. The conceptional-mathematical understanding for such an approach began to emerge only 30 years later. The strongest link between Jordan's view of QFT and modern "local quantum physics" is the central role of causal locality as the defining principle of QFT as opposed to the Born localization in QM. The issue of causal localization is also the arena where misunderstandings led to a serious derailment of large part of particle theory e.g. the misinterpretation of an infinite component pointlike field resulting from the quantization of the Nambu-Goto Lagrangian as a spacetime quantum string. The new concept of modular localization, which replaces Jordan's causal locality, is especially important to overcome the imperfections of gauge theories for which Jordan was the first to note nonlocal aspects of physical (not Lagrangian) charged fields. Two interesting subjects in which Jordan was far ahead of his contemporaries will be presented in two separate sections. Dedicated to my teacher and role model: Rudolf Haag.
Killing Vector Fields and Superharmonic Field Theories
Josua Groeger
2013-01-23
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, referred to as superharmonic action, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of the superharmonic 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.
Dark matter, Elko fields and Weinberg's quantum field theory formalism
Gillard, Adam
2010-01-01
The Elko quantum field was introduced by Ahluwalia and Grumiller, who proposed it as a candidate for dark matter. We study the Elko field in Weinberg's formalism for quantum field theory. We show that the most plausible attempt to make the Elko field fit into Weinberg's framework fails and we indicate some directions for future research.
Mathematical Inconsistencies in Dirac Field Theory
Dan Solomon; W. Oakton Skokie
1999-01-01
If a mathematical theory contains incompatible postulates then it is likely that the theory will produce theorems or results that are contradictory. It will be shown that this is the case with Dirac field theory. An example of such a contradiction is the problem asociated with evaluating the Schwinger term. It is generally known that different ways of evaluating this
Field theory models for tachyon and gauge field string dynamics
Joseph A. Minahan; Barton Zwiebach
2000-01-01
In hep-th\\/0008227, the unstable lump solution of phi3 theory was shown to have a spectrum governed by the solvable Schroedinger equation with the ell = 3 reflectionless potential and was used as a model for tachyon condensation in string theory. In this paper we study in detail an ellrightarrowinfty scalar field theory model whose lump solution mimics remarkably the string
Tachyon Matter in Boundary String Field Theory
Shigeki Sugimoto; Seiji Terashima
2002-01-01
We analyse the classical decay process of unstable D-branes in superstring theory using the boundary string field theory (BSFT) action. We show that the solutions of the equations of motion for the tachyon field asymptotically approach to T = x0 and the pressure rapidly falls off at late time producing the tachyon matter irrespective of the initial condition. We also
String Field Theory Around the Tachyon Vacuum
Leonardo Rastelli; Ashoke Sen; Barton Zwiebach
2000-01-01
Assuming that around the tachyon vacuum the kinetic term of cubic open string field theory is made purely of ghost operators we are led to gauge invariant actions which manifestly implement the absence of open string dynamics around this vacuum. We test this proposal by showing the existence of lump solutions of arbitrary codimension in this string field theory. The
Classical field theory. Advanced mathematical formulation
G. Sardanashvily
2009-03-04
In contrast with QFT, classical field theory can be formulated in strict mathematical terms of fibre bundles, graded manifolds and jet manifolds. Second Noether theorems provide BRST extension of this classical field theory by means of ghosts and antifields for the purpose of its quantization.
Numerical Object Oriented Quantum Field Theory Calculations
M. Williams
2009-05-07
The qft++ package is a library of C++ classes that facilitate numerical (not algebraic) quantum field theory calculations. Mathematical objects such as matrices, tensors, Dirac spinors, polarization and orbital angular momentum tensors, etc. are represented as C++ objects in qft++. The package permits construction of code which closely resembles quantum field theory expressions, allowing for quick and reliable calculations.
Axiomatic quantum field theory in curved spacetime
S. Hollands; R. M. Wald
2008-03-13
The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features--such as Poincare invariance and the existence of a preferred vacuum state--that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is locally and covariantly constructed from the spacetime metric), a microlocal spectrum condition, an "associativity" condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.
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.
Some convolution products in Quantum Field Theory
Herintsitohaina Ratsimbarison
2006-12-05
This paper aims to show constructions of scale dependence and interaction on some probabilistic models which may be revelant for renormalization theory in Quantum Field Theory. We begin with a review of the convolution product's use in the Kreimer-Connes formalism of perturbative renormalization. We show that the Wilson effective action can be obtained from a convolution product propriety of regularized Gaussian measures on the space of fields. Then, we propose a natural C*-algebraic framework for scale dependent field theories which may enhance the conceptual approach to renormalization theory. In the same spirit, we introduce a probabilistic construction of interacting theories for simple models and apply it for quantum field theory by defining a partition function in this setting.
Gauge Theory Wilson Loops and Conformal Toda Field Theory
Filippo Passerini
2010-03-15
The partition function of a family of four dimensional N=2 gauge theories has been recently related to correlation functions of two dimensional conformal Toda field theories. For SU(2) gauge theories, the associated two dimensional theory is A_1 conformal Toda field theory, i.e. Liouville theory. For this case the relation has been extended showing that the expectation value of gauge theory loop operators can be reproduced in Liouville theory inserting in the correlators the monodromy of chiral degenerate fields. In this paper we study Wilson loops in SU(N) gauge theories in the fundamental and anti-fundamental representation of the gauge group and show that they are associated to monodromies of a certain chiral degenerate operator of A_{N-1} Toda field theory. The orientation of the curve along which the monodromy is evaluated selects between fundamental and anti-fundamental representation. The analysis is performed using properties of the monodromy group of the generalized hypergeometric equation, the differential equation satisfied by a class of four point functions relevant for our computation.
Conformal nets and local field theory
Arthur Bartels; Christopher L. Douglas; André G. Henriques
2010-10-10
We describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between conformal field theories. Altogether we characterize the algebraic structure of the collection of conformal nets as a symmetric monoidal tricategory. Dualizable objects of this tricategory correspond to conformal-net-valued 3-dimensional local topological quantum field theories. We prove that the dualizable conformal nets are the finite sums of irreducible nets with finite \\mu-index. This classification provides a variety of 3-dimensional local field theories, including local field theories associated to central extensions of the loop groups of the special unitary groups.
Computer stochastics in scalar quantum field theory
Lang, C B
1993-01-01
This is a series of lectures on Monte Carlo results on the non-perturbative, lattice formulation approach to quantum field theory. Emphasis is put on 4D scalar quantum field theory. I discuss real space renormalization group, fixed point properties and logarithmic corrections, partition function zeroes, the triviality bound on the Higgs mass, finite size effects, Goldstone bosons and chiral perturbation theory, and the determination of scattering phase shifts for some scalar models.
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 ? and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.
Resonant Tunneling in Scalar Quantum Field Theory
S. -H. Henry Tye; Daniel Wohns
2009-10-06
The resonant tunneling phenomenon is well understood in quantum mechanics. We argue why a similar phenomenon must be present in quantum field theory. We then use the functional Schr\\"odinger method to show how resonant tunneling through multiple barriers takes place in quantum field theory with a single scalar field. We also show how this phenomenon in scalar quantum field theory can lead to an exponential enhancement of the single-barrier tunneling rate. Our analysis is carried out in the thin-wall approximation.
Space–time noncommutative field theories and unitarity
Jaume Gomis; Thomas Mehen
2000-01-01
We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space–time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On the other hand, there
Analytical mechanics and field theory: derivation of equations from energy conservation
NASA Astrophysics Data System (ADS)
Vinokurov, N. A.
2014-06-01
Equations of motion in mechanics and field equations in field theory are conventionally derived using the least action principle. This paper presents a nonvariational derivation of Hamilton's and Lagrange's equations. The derivation starts by specifying the system energy as a function of generalized coordinates and velocities and then introduces generalized momenta in such a way that the energy remains unchanged under variations of any degree of freedom. This immediately leads to Hamilton's equations with an as yet undefined Hamiltonian. The explicit dependence of generalized momenta on the coordinates and velocities is determined by first finding the Lagrangian from the known energy function. We discuss electrodynamics as an illustrative example. The proposed approach provides new insight into the nature of canonical momenta and offers a way to find the Lagrangian from the known energy of the system.
Unified field theories and Einstein
S C Tiwari
2006-02-16
Einstein's contribution to relativity is reviewed. It is pointed out that Weyl gave first unified theory of gravitation and electromagnetism and it was different than the five dimensional theory of Kaluza. Einstein began his work on unification in 1925 that continued whole through the rest of his life.
Relativistic Theory of Infinite Statistics Fields
Chao Cao; Yi-Xin Chen; Jian-Long Li
2009-05-19
Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. However, the validity of relativistic quon theories is still in doubt. In this paper we prove that there exists a relativistic quantum field theory which allows interactions involving infinite statistics particles. We also give some consistency analysis of this theory such as conservation of statistics and Feynman rules.
E. Lévêque; L. Chevillard; J.-F. Pinton; S. Roux; A. Arnéodo; N. Mordant
2007-01-01
Three temporal velocity signals are analyzed from direct numerical simulations of the Navier–Stokes (N–S) equations. The three signals are: (i) the velocity of fluid particles transported by the time-evolving solution (Eulerian velocity field) of the N–S equations, referred to as the dynamic case; (ii) the velocity of fluid particles transported by a solution of the N–S equations at some fixed
Atomic Probes of Noncommutative Field Theory
Charles D. Lane
2002-01-07
We consider the role of Lorentz symmetry in noncommutative field theory. We find that a Lorentz-violating standard-model extension involving ordinary fields is general enough to include any realisitc noncommutative field theory as a subset. This leads to various theoretical consequences, as well as bounds from existing experiments at the level of (10 TeV)$^{-2}$ on the scale of the noncommutativity parameter.
Metric Quantum Field Theory: a Preliminary Look.
NASA Astrophysics Data System (ADS)
Watson, William Nathan
1988-12-01
Spacetime coordinates are involved in uncertainty relations; spacetime itself appears to exhibit curvature. Could the continua associated with field variables exhibit curvature? This question, as well as the ideas that (a) difficulties with quantum theories of gravitation may be due to their formulation in an incorrect analogy with other quantum field theories, (b) spacetime variables should not be any more basic than others for describing physical phenomena, and (c) if field continua do not exhibit curvature, the reasons would be of interest, motivated the formulation of a theory of variable curvature and torsion in the electromagnetic four-potential's reciprocal space. Curvature and torsion equation completely analogous to those for a gauge theory of gravitation (the Einstein-Cartan-Sciama-Kibble theory) are assumed for this continuum. The interaction-Hamiltonian density of this theory, to a first approximation, implies that in addition to the Maxwell-Dirac field interaction of ordinary quantum electrodynamics, there should also be an interaction between Dirac-field vector and pseudovector currents unmediated by photons, as well as other interactions involving two or three Dirac-field currents interacting with the Maxwell field at single spacetime events (the expressions for which involve an inverse Maxwell-field operator of as-yet obscure import). Calculations expressing Bhabha-scattering cross sections for incident beams with parallel spins differ from those of unmodified quantum electrodynamics by terms of first order in the "gravitational constant" of the theory, but the corresponding cross section for unpolarized incident beams differs from that of the unmodified theory only by terms of higher order in that constant. Undesirable features of the present theory include its nonrenormalizability, the obscurity of the meaning of its inverse field operator, and its being based on electrodynamics rather than electroweak dynamics. Prospects include the possibility that a theory of this type may help explain recently-observed spin-dependent effects in proton-proton scattering. The calculations show that nonspacetime curvatures could be physically manifested.
J. Greensite
1995-08-14
It is shown that the classical field equations pertaining to gravity coupled to other bosonic fields are equivalent to a single geodesic equation, describing the free fall of a point particle in superspace. Some implications for quantum gravity are discussed.
The implications of naturalness in effective field theory on the masses of resonances
Dugan, M J; Dugan, Michael J.; Golden, Mitchell
1993-01-01
Many years ago Weinberg formulated a definition of ``naturalness'' for effective theories: if an effective theory is to make sense, coefficients must not change too much when the cutoff scale is changed by a factor of order 1. As an example, we consider simple field theories in which an $O(N)$ symmetry spontaneously breaks to $O(N-1)$. We show that in these theories Weinberg's criterion for a natural effective theory may be applied directly to the $S$-matrix; it implies that the scale of new physics, beyond the Goldstone bosons, may not be too large: there is always a particle or a cut of mass below or about $4 \\pi f / \\sqrt{N}$. We discuss the range of convergence of the expansion of the chiral Lagrangian. It appears to be impossible to construct an underlying theory of the type considered here that fails to satisfy Weinberg's criterion.
Valuation theory of exponential Hardy fields
Kuhlmann, Franz-Viktor
2012-01-01
We describe the residue fields of arbitrary convex valuations on certain o-minimal expansions of the ordered field of real numbers. References: [1] Franz-Viktor and Salma Kuhlmann: Residue fields of arbitrary convex valuations on restricted analytic fields with exponentiation I, The Fields Institute Preprint Series (1997). [2] Franz-Viktor and Salma Kuhlmann: Valuation theory of exponential Hardy fields I, Mathematische Zeitschrift 243, 671--688 (2003) [3] Ordered Exponential Fields, by Salma Kuhlmann, The Fields Institute Monograph Series Vol. 12, (2000).
Quantum Field Theory for Mathematicians Hamiltonian Mechanics and Symplectic Geometry
Woit, Peter
Quantum Field Theory for Mathematicians · Hamiltonian Mechanics and Symplectic Geometry Integral Quantization Supersymmetric Quantum Mechanics Introduction to Scattering Theory · Classical Field Theory · Relativistic Fields, Poincar´e Group and Wigner Classification · Free Quantum Fields
Supergeometry in locally covariant quantum field theory
Hack, Thomas-Paul; Schenkel, Alexander
2015-01-01
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 --> 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 --> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the en...
Cosmological implications of conformal field theory
Nesbet, R K
2009-01-01
Requiring all elementary fields to have conformal scaling symmetry removes a formal conflict between Einstein-Hilbert gravitational theory and the quantum theory of elementary particles and fields. Higgs symmetry-breaking requires a nonvanishing scalar field throughout spacetime, a cosmological entity. In uniform, isotropic geometry, conformal gravitational theory that includes this scalar field determines a modified Friedmann evolution equation with nonvanishing cosmological constant. Numerical solution determines parameters consistent with empirical data for redshifts $z\\leq z_*=1090$, including luminosity distances for observed type Ia supernovae and peak structure ratios in the cosmic microwave background (CMB). In this theory, a cosmological constant within current empirical error bounds implies extremely small mass for the Higgs boson. A simplified but internally consistent model of nucleosynthesis determines baryon number density from the empirical CMB temperature and acoustic wave velocity. The theory...
Symmetries, Newtonoid Vector Fields and Conservation Laws in the Lagrangian k-SYMPLECTIC Formalism
NASA Astrophysics Data System (ADS)
Bua, Lucía; Bucataru, Ioan; Salgado, Modesto
2012-11-01
In this paper, we study symmetries, Newtonoid vector fields, conservation laws, Noether's theorem and its converse, in the framework of the k-symplectic formalism, using the Frölicher-Nijenhuis formalism on the space of k1-velocities of the configuration manifold. For the case k = 1, it is well known that Cartan symmetries induce and are induced by constants of motions, and these results are known as Noether's theorem and its converse. For the case k > 1, we provide a new proof for Noether's theorem, which shows that, in the k-symplectic formalism, each Cartan symmetry induces a conservation law. We prove that, under some assumptions, the converse of Noether's theorem is also true and we provide examples when this is not the case. We also study the relations between dynamical symmetries, Newtonoid vector fields, Cartan symmetries and conservation laws, showing when one of them will imply the others. We use several examples of partial differential equations to illustrate when these concepts are related and when they are not.
Perturbative Deformations of Conformal Field Theories Revisited
NASA Astrophysics Data System (ADS)
Kriz, Igor
The purpose of this paper is to revisit the theory of perturbative deformations of conformal field theory from a mathematically rigorous, purely worldsheet point of view. We specifically include the case of N = (2,2) conformal field theories. From this point of view, we find certain surprising obstructions, which appear to indicate that contrary to previous findings, not all deformations along marginal fields exist perturbatively. This includes the case of deformation of the Gepner model of the Fermat quintic along certain cc fields. In other cases, including Gepner models of K3-surfaces and the free field theory, our results coincides with known predictions. We give partial interpretation of our results via renormalization and mirror symmetry.
Computational Methods in Quantum Field Theory
Kurt Langfeld
2007-11-19
After a brief introduction to the statistical description of data, these lecture notes focus on quantum field theories as they emerge from lattice models in the critical limit. For the simulation of these lattice models, Markov chain Monte-Carlo methods are widely used. We discuss the heat bath and, more modern, cluster algorithms. The Ising model is used as a concrete illustration of important concepts such as correspondence between a theory of branes and quantum field theory or the duality map between strong and weak couplings. The notes then discuss the inclusion of gauge symmetries in lattice models and, in particular, the continuum limit in which quantum Yang-Mills theories arise.
Some differences between Dirac's hole theory and quantum field theory
Dan Solomon; W. Oakton Skokie
2005-01-01
Dirac's hole theory (HT) and quantum field theory (QFT) are generally considered equivalent. However, it was recently shown by several investigators that this is not necessarily the case because when the change in the vacuum energy was calculated for a time-independent perturbation, HT and QFT yielded different results. In this paper, we extend this discussion to include a time-dependent perturbation
Twisted Poincare invariant quantum field theories
Balachandran, A. P.; Qureshi, B. A. [Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States); Pinzul, A. [Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, Sao Paulo, SP, 05315-970 (Brazil)
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.
Generating functionals and Lagrangian partial differential equations
Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin [Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, California 92093-0112 (United States)] [Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, California 92093-0112 (United States)
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.
NASA Astrophysics Data System (ADS)
Zumalacárregui, Miguel; García-Bellido, Juan
2014-03-01
We study the structure of scalar-tensor theories of gravity based on derivative couplings between the scalar and the matter degrees of freedom introduced through an effective metric. Such interactions are classified by their tensor structure into conformal (scalar), disformal (vector), and extended disformal (traceless tensor), as well as by the derivative order of the scalar field. Relations limited to first derivatives of the field ensure second-order equations of motion in the Einstein frame and hence the absence of Ostrogradski ghost degrees of freedom. The existence of a mapping to the Jordan frame is not trivial in the general case, and can be addressed using the Jacobian of the frame transformation through its eigenvalues and eigentensors. These objects also appear in the study of different aspects of such theories, including the metric and field redefinition transformation of the path integral in the quantum mechanical description. Although second-order in the Einstein frame, generic disformally coupled theories are described by higher-order equations of motion in the Jordan frame. This apparent contradiction is solved by the use of a hidden constraint: the contraction of the metric equations with a Jacobian eigentensor provides a constraint relation for the higher field derivatives, which allows one to express the dynamical equations in a second-order form. This signals a loophole in Horndeski's theorem and allows one to enlarge the set of scalar-tensor theories which are Ostrogradski stable. The transformed Gauss-Bonnet terms are also discussed for the simplest conformal and disformal relations.
Interaction of higher spin massive fields with gravity in string theory
V. D. Pershin
2000-09-29
Derivations of consistent equations of motion for the massive spin two field interacting with gravity is reviewed. From the field theoretical point of view the most general classical action describing consistent causal propagation in vacuum Einstein spacetime is given. It is also shown that the massive spin two field can be consistently described in arbitrary background by means of lagrangian equations representing an infinite series in curvature. Within string theory equations of motion for the massive spin two field coupled to gravity is derived from the requirement of quantum Weyl invariance of the corresponding two dimensional sigma-model. In the lowest order in string length the effective equations of motion are demonstrated to coincide with the general form of consistent equations derived in field theory.
Stochastic modeling of Lagrangian accelerations
NASA Astrophysics Data System (ADS)
Reynolds, Andy
2002-11-01
It is shown how Sawford's second-order Lagrangian stochastic model (Phys. Fluids A 3, 1577-1586, 1991) for fluid-particle accelerations can be combined with a model for the evolution of the dissipation rate (Pope and Chen, Phys. Fluids A 2, 1437-1449, 1990) to produce a Lagrangian stochastic model that is consistent with both the measured distribution of Lagrangian accelerations (La Porta et al., Nature 409, 1017-1019, 2001) and Kolmogorov's similarity theory. The later condition is found not to be satisfied when a constant dissipation rate is employed and consistency with prescribed acceleration statistics is enforced through fulfilment of a well-mixed condition.
MEDSLIK-II, a Lagrangian marine surface oil spill model for short-term forecasting - Part 1: Theory
NASA Astrophysics Data System (ADS)
De Dominicis, M.; Pinardi, N.; Zodiatis, G.; Lardner, R.
2013-11-01
The processes of transport, diffusion and transformation of surface oil in seawater can be simulated using a Lagrangian model formalism coupled with Eulerian circulation models. This paper describes the formalism and the conceptual assumptions of a Lagrangian marine surface oil slick numerical model and rewrites the constitutive equations in a modern mathematical framework. The Lagrangian numerical representation of the oil slick requires three different state variables: the slick, the particle and the structural state variables. Transformation processes (evaporation, spreading, dispersion and coastal adhesion) act on the slick state variables, while particle variables are used to model the transport and diffusion processes. The slick and particle variables are recombined together to compute the oil concentration in water, a structural state variable. The mathematical and numerical formulation of oil transport, diffusion and transformation processes described in this paper, together with the many simplifying hypothesis and parameterizations, form the basis of a new, open source Lagrangian surface oil spill model, the so-called MEDSLIK-II, based on its precursor MEDSLIK (Lardner et al., 1998, 2006; Zodiatis et al., 2008a). Part 2 of this paper describes the applications of the model to oil spill simulations that allow the validation of the model results and the study of the sensitivity of the simulated oil slick to different model numerical parameterizations.
MEDSLIK-II, a Lagrangian marine oil spill model for short-term forecasting - Part 1: Theory
NASA Astrophysics Data System (ADS)
De Dominicis, M.; Pinardi, N.; Zodiatis, G.
2013-03-01
The processes of transport, diffusion and transformation of surface oil in seawater can be simulated using a Lagrangian model formalism coupled with Eulerian circulation models. This paper describes the formalism and the conceptual assumptions of a Lagrangian marine oil slick numerical model and re-writes the constitutive equations in a modern mathematical framework. The Lagrangian numerical representation of the oil slick requires three different state variables: the slick, the particle and the structural state variables. Transformation processes (evaporation, spreading, dispersion and coastal adhesion) act on the slick state variables, while particles variables are used to model the transport and diffusion processes. The slick and particle variables are recombined together to compute the oil concentration in water, a structural state variable. The mathematical and numerical formulation of oil transport, diffusion and transformation processes described in this paper, together with the many simplifying hypothesis and parameterizations, form the basis of a new, open source Lagrangian surface oil spill model, so-called MEDSLIK-II. Part 2 of this paper describes the applications of MEDSLIK-II to oil spill simulations that allow the validation of the model results and the study of the sensitivity of the simulated oil slick to different model numerical parameterizations.
Zero Dimensional Field Theory of Tachyon Matter
D. D. Dimitrijevic; G. S. Djordjevic
2006-11-28
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.
Zero Dimensional Field Theory of Tachyon Matter
Dimitrijevic, D. D. [Institute of Physics, Faculty of Sciences, Nis (Serbia); Djordjevic, G. S. [Department of Physics, University of Nis, P.O.Box 224, Nis (Serbia)
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.
Heavy quarks in effective field theories
Jain, Ambar
2009-01-01
Heavy quark physics serves as a probe to understand QCD, measure standard model parameters, and look for signs of new physics. We study several aspects of heavy quark systems in an effective field theory framework, including ...
Tachyon condensation in string field theory
Moeller, Nicolas, 1975-
2003-01-01
In this thesis, we present some results that strongly support Sen's conjectures on tachyon condensation on a bosonic D-brane. Our main tool of analysis is level truncated open bosonic string field theory We use level ...
Effective Field Theory for Nuclear Physics
David B. Kaplan
1999-01-01
I summarize the motivation for the effective field theory approach to nuclear physics, and highlight some of its recent accomplishments. The results are compared with those computed in potential models.
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.
Spinless Quantum Field Theory and Interpretation
Dong-Sheng Wang
2013-03-07
Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the Klein-Gordon equation, and we find that there exists a Dirac form of this equation which predicts the existence of spinless fermion. For its understanding, we start from the interpretation of quantum field based on the concept of quantum scope, we also extract new meanings of wave-particle duality and quantum statistics. The existence of spinless fermion is consistent with spin-statistics theorem and also supersymmetry, and it leads to several new kinds of interactions among elementary particles. Our work contributes to the study of spinless quantum field theory and could have implications for the case of higher spin.
Harvesting CMB information via field theory
NASA Astrophysics Data System (ADS)
Ensslin, Torsten A.; Oppermann, Niels; Dorn, Sebastian; Böhm, Vanessa
2015-08-01
The CMB is a high fidelity information source on cosmology and astrophysics. The extraction of information has to take into account the field nature of the CMB radiation field as well as the statistical properties of the CMB and its foregrounds. This can naturally be done via information field theory (IFT), the theory on how to infer field properties from incomplete and noisy measurements. IFT is introduced in this talk to address a variety of CMB-related inference problems, such as optimally measuring primordial non-Gaussianity, reconstructing the primordial and evolved gravitational potential of the Universe, and the separation of foreground contaminants.
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.
Holographic applications of logarithmic conformal field theories
D. Grumiller; W. Riedler; J. Rosseel; T. Zojer
2013-02-27
We review the relations between Jordan cells in various branches of physics, ranging from quantum mechanics to massive gravity theories. Our main focus is on holographic correspondences between critically tuned gravity theories in Anti-de Sitter space and logarithmic conformal field theories in various dimensions. We summarize the developments in the past five years, include some novel generalizations and provide an outlook on possible future developments.
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 ?4 theory in the ? expansion.
Conserved Currents of Double Field Theory
Blair, Chris D A
2015-01-01
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.
Mathematical renormalization of Hamiltonian field theories
A. V. Stoyanovsky
2015-06-18
We rigorously define renormalized evolution operator of the Schr\\"odinger equation in the infinite dimensional Weyl-Moyal algebra for any time interval for arbitrary Hamiltonian depending on time. We state that for renormalizable field theories, in the interaction representation, and for the time interval being the full real axis, our construction yields standard renormalized $S$-matrix and Green functions of perturbative quantum field theory.
Tachyon Matter in Boundary String Field Theory
S. Sugimoto; S. Terashima
2002-05-18
We analyse the classical decay process of unstable D-branes in superstring theory using the boundary string field theory (BSFT) action. We show that the solutions of the equations of motion for the tachyon field asymptotically approach to T=x^0 and the pressure rapidly falls off at late time producing the tachyon matter irrespective of the initial condition. We also consider the cosmological evolution driven by the rolling tachyon using the BSFT action as an effective action.
Einstein manifolds and conformal field theories
Steven S. Gubser
1999-01-01
In light of the anti-de Sitter space conformal field theory correspondence, it is natural to try to define a conformal field theory in a large N, strong coupling limit via a supergravity compactification on the product of an Einstein manifold and anti-de Sitter space. We consider the five-dimensional manifolds Tpq which are coset spaces [SU(2)×SU(2)]\\/U(1). The central charge and a
Quantum field theory on LQC Bianchi spacetimes
Andrea Dapor; Jerzy Lewandowski; Yaser Tavakoli
2013-05-20
Quantum theory of a scalar field is developed on the LQC Bianchi I space-time. By comparing the the quantum field theory for a single mode on classical and quantum background geometries we find that an effective Bianchi I space-time emerges. We show that by disregarding the back-reaction no Lorentz-violation is present, despite the effective metric being different than the classical Bianchi I one.
Derivative expansions for affinely quantized field theories
Carl M. Bender; R. J. Rivers; C. C. Wong
1990-01-01
We examine the existence of an affinely (noncanonically) quantized free scalar theory via an expansion in powers of derivatives of the field. We show that with the simplest choice of measure affine quantization does not provide a useful basis for a nontrivial, well-defined theory.
Pion masses in quasiconformal gauge field theories
Dietrich, Dennis D.; Jaervinen, Matti
2009-03-01
We study modifications to Weinberg-like sum rules in quasiconformal gauge field theories. Beyond the two Weinberg sum rules and the oblique S parameter, we study the pion mass and the X parameter. Especially, we evaluate the pion mass for walking technicolor theories, in particular, minimal walking technicolor, and find contributions of the order of up to several hundred GeV.
A Count of Classical Field Theory Graphs
Gordon Chalmers
2005-07-28
A generating function is derived that counts the number of diagrams in an arbitrary scalar field theory. The number of graphs containing any number $n_j$ of $j$-point vertices is given. The count is also used to obtain the number of classical graphs in gauge theory and gravity.
Pion masses in quasiconformal gauge field theories
Dennis D. Dietrich; Matti Jarvinen
2009-01-22
We study modifications to Weinberg-like sum rules in quasiconformal gauge field theories. Beyond the two Weinberg sum rules and the oblique S parameter we study the pion mass and the X parameter. Especially, we evaluate the pion mass for walking technicolour theories, in particular also minimal walking technicolour, and find contributions of the order of up to several hundred GeV.
Pion masses in quasiconformal gauge field theories
Dietrich, Dennis D
2009-01-01
We study modifications to Weinberg-like sum rules in quasiconformal gauge field theories. Beyond the two Weinberg sum rules and the oblique S parameter we study the pion mass and the X parameter. Especially, we evaluate the pion mass for walking technicolour theories, in particular also minimal walking technicolour, and find contributions of the order of up to several hundred GeV.
Particle Physics and Introduction to Field Theory
T. D. Lee; Sidney Drell
1981-01-01
The gamut of modern particle physics is presented. Topics included are a self-contained introduction to standard quantum field theory, a discussion of solitons, a detailed discussion of symmetry principles in particle physics, including symmetry breaking, and the formalism and physical ideas of non-Abelain gauge theories and Quantum Chromodynamics. Recent original research by the author is presented. The book concludes with
RATIONAL SYMPLECTIC FIELD THEORY FOR LEGENDRIAN KNOTS
Ng, Lenny
, Symplectic Field Theory (SFT), which was introduced by Eliashberg, Givental, and Hofer about a decade ago [EGH00]. The relevant portion of the SFT package for our purposes is a filtered theory for contact puncture, SFT counts holomorphic curves with arbitrarily many positive punctures. In the "closed" case (in
General Covariance in Algebraic Quantum Field Theory
Romeo Brunetti; Martin Porrmann; Giuseppe Ruzzi
2005-12-17
In this review we report on how the problem of general covariance is treated within the algebraic approach to quantum field theory by use of concepts from category theory. Some new results on net cohomology and superselection structure attained in this framework are included.
The zero-bin and mode factorization in quantum field theory
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 statistical correlations in thermal field theories: Boundary effective theory
Bessa, A. [Escola de Ciencias e Tecnologia, Universidade Federal do Rio Grande do Norte, Caixa Postal 1524, 59072-970, Natal, RN (Brazil); Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP (Brazil); Brandt, F. T. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP (Brazil); Carvalho, C. A. A. de; Fraga, E. S. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972, Rio de Janeiro, RJ (Brazil)
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.
Simple recursion relations for general field theories
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Shen, Chia-Hsien; Trnka, Jaroslav
2015-06-01
On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-line constructibility of all gauge theories with fermions and complex scalars in arbitrary representations, all supersymmetric theories, and the standard model. Moreover, all amplitudes in non-renormalizable theories without derivative interactions are constructible; with derivative interactions, a subset of amplitudes is constructible. We illustrate our results with examples from both renormalizable and non-renormalizable theories. Our study demonstrates both the power and limitations of recursion relations as a self-contained formulation of quantum field theory.
Nonlinear field theories during homogeneous spatial dilation
Carlos Escudero
2013-09-22
The effect of a uniform dilation of space on stochastically driven nonlinear field theories is examined. This theoretical question serves as a model problem for examining the properties of nonlinear field theories embedded in expanding Euclidean Friedmann-Lema\\^{\\i}tre-Robertson-Walker metrics in the context of cosmology, as well as different systems in the disciplines of statistical mechanics and condensed matter physics. Field theories are characterized by the speed at which they propagate correlations within themselves. We show that for linear field theories correlations stop propagating if and only if the speed at which the space dilates is higher than the speed at which correlations propagate. The situation is in general different for nonlinear field theories. In this case correlations might stop propagating even if the velocity at which space dilates is lower than the velocity at which correlations propagate. In particular, these results imply that it is not possible to characterize the dynamics of a nonlinear field theory during homogeneous spatial dilation {\\it a priori}. We illustrate our findings with the nonlinear Kardar-Parisi-Zhang equation.
Dark matter, Elko fields and Weinberg's quantum field theory formalism
Adam Gillard; Benjamin Martin
2012-05-08
The Elko quantum field was introduced by Ahluwalia and Grumiller, who proposed it as a candidate for dark matter. We study the Elko field in Weinberg's formalism for quantum field theory. We prove that if one takes the symmetry group to be the full Poincar\\'e group then the Elko field is not a quantum field in the sense of Weinberg. This confirms results of Ahluwalia, Lee and Schritt, who showed using a different approach that the Elko field does not transform covariantly under rotations and hence has a preferred axis.
Dark Matter, Elko Fields and Weinberg's Quantum Field Theory Formalism
NASA Astrophysics Data System (ADS)
Gillard, Adam; Martin, Benjamin
2012-02-01
The Elko quantum field was introduced by Ahluwalia and Grumiller, who proposed it as a candidate for dark matter. We study the Elko field in Wemberg's formalism for quantum field theory. We prove that if one takes the symmetry group to be the full Pomcaré group then the Elko field is not a quantum field in the sense of Weinberg. This confirms results of Ahluwalia, Lee and Schritt, who showed using a different approach that the Elko field does not transform covariantly under rotations and hence has a preferred axis.
Exterior Differential Systems for Field Theories
Frank B. Estabrook
2015-02-24
Exterior Differential Systems (EDS) and Cartan forms, set in the state space of field variables taken together with four space-time variables, are formulated for classical gauge theories of Maxwell and SU(2) Yang-Mills fields minimally coupled to Dirac spinor multiplets. Cartan character tables are calculated, showing whether the EDS, and so the Euler-Lagrange partial differential equations, is well-posed. The first theory, with 22 dimensional state space (10 Maxwell field and potential components and 8 components of a Dirac field), anticipates QED. In the second, non-Abelian, case (30 Yang-Mills field components and 16 Dirac), only if three additional "ghost" fields are included (15 more scalar variables) is a well-posed EDS found. This classical formulation anticipates the need for introduction of Fadeev-Popov ghost fields in the quantum standard model.
Dark energy or modified gravity? An effective field theory approach
Bloomfield, Jolyon; Flanagan, Éanna É. [Center for Radiophysics and Space Research, Cornell University, Ithaca, NY 14853 (United States); Park, Minjoon [Department of Physics, University of Massachusetts, Amherst, MA 01003 (United States); Watson, Scott, E-mail: jkb84@cornell.edu, E-mail: eef3@cornell.edu, E-mail: minjoonp@physics.umass.edu, E-mail: gswatson@syr.edu [Department of Physics, Syracuse University, Syracuse, NY 13244 (United States)
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 ?CDM, 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.
Branes and supersymmetric quantum field theories
NASA Astrophysics Data System (ADS)
Park, Chan Youn
Since the discovery of D-branes as non-perturbative, dynamic objects in string theory, various configurations of branes in type IIA/B string theory and M-theory have been considered to study their low-energy dynamics described by supersymmetric quantum field theories. One example of such a construction is based on the description of Seiberg-Witten curves of four-dimensional N = 2 supersymmetric gauge theories as branes in type IIA string theory and M-theory. This enables us to study the gauge theories in strongly-coupled regimes. Spectral networks are another tool for utilizing branes to study non-perturbative regimes of two- and four-dimensional supersymmetric theories. Using spectral networks of a Seiberg-Witten theory we can find its BPS spectrum, which is protected from quantum corrections by supersymmetry, and also the BPS spectrum of a related two-dimensional N = (2,2) theory whose (twisted) superpotential is determined by the Seiberg-Witten curve. When we don't know the perturbative description of such a theory, its spectrum obtained via spectral networks is a useful piece of information. In this thesis we illustrate these ideas with examples of the use of Seiberg-Witten curves and spectral networks to understand various two- and four-dimensional supersymmetric theories. First, we examine how the geometry of a Seiberg-Witten curve serves as a useful tool for identifying various limits of the parameters of the Seiberg-Witten theory, including Argyres-Seiberg duality and Argyres-Douglas fixed points. Next, we consider the low-energy limit of a two-dimensional N = (2, 2) supersymmetric theory from an M-theory brane configuration whose (twisted) superpotential is determined by the geometry of the branes. We show that, when the two-dimensional theory flows to its infra-red fixed point, particular cases realize Kazama-Suzuki coset models. We also study the BPS spectrum of an Argyres-Douglas type superconformal field theory on the Coulomb branch by using its spectral networks. We provide strong evidence of the equivalence of superconformal field theories from different string-theoretic constructions by comparing their BPS spectra.
Superstring field theory equivalence: Ramond sector
NASA Astrophysics Data System (ADS)
Kroyter, Michael
2009-10-01
We prove that the finite gauge transformation of the Ramond sector of the modified cubic superstring field theory is ill-defined due to collisions of picture changing operators. Despite this problem we study to what extent could a bijective classical correspondence between this theory and the (presumably consistent) non-polynomial theory exist. We find that the classical equivalence between these two theories can almost be extended to the Ramond sector: We construct mappings between the string fields (NS and Ramond, including Chan-Paton factors and the various GSO sectors) of the two theories that send solutions to solutions in a way that respects the linearized gauge symmetries in both sides and keeps the action of the solutions invariant. The perturbative spectrum around equivalent solutions is also isomorphic. The problem with the cubic theory implies that the correspondence of the linearized gauge symmetries cannot be extended to a correspondence of the finite gauge symmetries. Hence, our equivalence is only formal, since it relates a consistent theory to an inconsistent one. Nonetheless, we believe that the fact that the equivalence formally works suggests that a consistent modification of the cubic theory exists. We construct a theory that can be considered as a first step towards a consistent RNS cubic theory.
Currents and the Energy-Momentum Tensor in Classical Field Theory: A fresh look at an Old Problem
Michael Forger; Hartmann Römer
2003-07-21
We give a comprehensive review of various methods to define currents and the energy-momentum tensor in classical field theory, with emphasis on a geometric point of view. The necessity of ``improving'' the expressions provided by the canonical Noether procedure is addressed and given an adequate geometric framework. The main new ingredient is the explicit formulation of a principle of ``ultralocality'' with respect to the symmetry generators, which is shown to fix the ambiguity inherent in the procedure of improvement and guide it towards a unique answer: when combined with the appropriate splitting of the fields into sectors, it leads to the well-known expressions for the current as the variational derivative of the matter field Lagrangian with respect to the gauge field and for the energy-momentum tensor as the variational derivative of the matter field Lagrangian with respect to the metric tensor. In the second case, the procedure is shown to work even when the matter field Lagrangian depends explicitly on the curvature, thus establishing the correct relation between scale invariance, in the form of local Weyl invariance ``on shell'', and tracelessness of the energy-momentum tensor, required for a consistent definition of the concept of a conformal field theory.
Power counting in nuclear effective field theory
NASA Astrophysics Data System (ADS)
Valderrama, M. Pavon
2015-10-01
The effective field theory formulation of nuclear forces is able to provide a systematic and model independent description of nuclear physics, where all processes involving nucleons and pions can be described in terms of the same set of couplings, the theoretical errors are known in advance and the connection with QCD is present. These features are a consequence of renormalization group invariance, which in turn determines the power counting of the theory. Here we present a brief outline of how to determine the power counting of nuclear effective field theory, what does it looks like and what are the predictions for the two-nucleon sector at lowest orders.
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 (?(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
D-branes and string field theory
Sigalov, Ilya
2006-01-01
In this thesis we study the D-brane physics in the context of Witten's cubic string field theory. We compute first few terms the low energy effective action for the non-abelian gauge field A, from Witten's action. We show ...
Algebras without Involution and Quantum Field Theories
Glenn Eric Johnson
2014-10-01
Explicit realizations of quantum field theory (QFT) are admitted by a revision to the Wightman axioms for the vacuum expectation values (VEV) of fields. The technical development of QFT is expanded beyond positive functionals on *-algebras while the physically motivated properties: Poincare covariance; positive energy; microcausality; and a Hilbert space realization of states, are preserved.
Nonperturbative Quantum Field Theory in Astrophysics
Dan Mazur
2012-09-20
The extreme electromagnetic or gravitational fields associated with some astrophysical objects can give rise to macroscopic effects arising from the physics of the quantum vacuum. Therefore, these objects are incredible laboratories for exploring the physics of quantum field theories. In this dissertation, we explore this idea in three astrophysical scenarios.
Casimir Effects in Renormalizable Quantum Field Theories
Noah Graham; Robert L. Jaffe; Herbert Weigel
2002-01-01
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
Chiral effective field theory and nuclear forces
R. Machleidt; D. R. Entem
2011-05-15
We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.
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.
Noncommutative Tachyons And String Field Theory
Witten, Edward
2000-01-01
It has been shown recently that by turning on a large noncommutativity parameter, the description of tachyon condensation in string theory can be drastically simplified. We reconsider these issues from the standpoint of string field theory, showing that, from this point of view, the key fact is that in the limit of a large B-field, the string field algebra factors as the product of an algebra that acts on the string center of mass only and an algebra that acts on all other degrees of freedom carried by the string.
Phase-space quantization of field theory.
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
Parafermionic conformal field theory on the lattice
NASA Astrophysics Data System (ADS)
Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul
2014-11-01
Finding the precise correspondence between lattice operators and the continuum fields that describe their long-distance properties is a largely open problem for strongly interacting critical points. Here, we solve this problem essentially completely in the case of the three-state Potts model, which exhibits a phase transition described by a strongly interacting ‘parafermion’ conformal field theory. Using symmetry arguments, insights from integrability, and extensive simulations, we construct lattice analogues of nearly all the relevant and marginal physical fields governing this transition. This construction includes chiral fields such as the parafermion. Along the way we also clarify the structure of operator product expansions between order and disorder fields, which we confirm numerically. Our results both suggest a systematic methodology for attacking non-free field theories on the lattice and find broader applications in the pursuit of exotic topologically ordered phases of matter.
Paolo Pasti; Igor Samsonov; Dmitri Sorokin; Mario Tonin
2009-01-01
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.JHEPFG1029-8479 06 (2008) 105.10.1088\\/1126-6708\\/2008\\/06\\/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
Codimension two lump solutions in string field theory and tachyonic theories
Nicolas Moeller
2000-08-11
We present some solutions for lumps in two dimensions in level-expanded string field theory, as well as in two tachyonic theories: pure tachyonic string field theory and pure $\\phi^3$ theory. Much easier to handle, these theories might be used to help understanding solitonic features of string field theory. We compare lump solutions between these theories and we discuss some convergence issues.
Codimension two lump solutions in string field theory and tachyonic theories
Nicolas Moeller
2000-01-01
We present some solutions for lumps in two dimensions in level-expanded string field theory, as well as in two tachyonic theories: pure tachyonic string field theory and pure $\\\\phi^3$ theory. Much easier to handle, these theories might be used to help understanding solitonic features of string field theory. We compare lump solutions between these theories and we discuss some convergence
"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.
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.
Thermo-Field Extension of Open String Field Theory
Cantcheff, M Botta
2015-01-01
We study the implementation of Thermo Field Dynamics (TFD) to the covariant formulation of Open String Field Theory (OSFT). In this paper, we extend the state space and fields according to the duplication rules of TFD and construct the corresponding classical action. The result is a theory whose fields would encode the statistical information of open strings and, noticeably, present degrees of freedom that could be identified as those of closed strings. The physical spectrum of the free theory is studied through the cohomology of the extended BRST charge, and, as a result, we get new fields in the spectrum. 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 many 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 whose results at tree-level amplitudes agree with those of the conventi...
Alternative expression for the electromagnetic Lagrangian
Saldanha, Pablo L
2015-01-01
We propose an alternative expression for the Lagrangian density that governs the interaction of a charged particle with external electromagnetic fields. The proposed 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. The total Lagrangian for a set of charged particles assumes a simple elegant form with the alternative formulation, giving an aesthetic support for it. The proposed Lagrangian is equivalent to the traditional one in their domain of validity and provides an interesting description of the Aharonov-Bohm effect.
Simple Recursion Relations for General Field Theories
Cheung, Clifford; Trnka, Jaroslav
2015-01-01
On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-...
Exceptional field theory: SO(5,5)
NASA Astrophysics Data System (ADS)
Abzalov, Aidar; Bakhmatov, Ilya; Musaev, Edvard T.
2015-06-01
We construct Exceptional Field Theory for the group SO(5, 5) based on the extended (6+16)-dimensional spacetime, which after reduction gives the maximal D = 6 supergravity. We present both a true action and a duality-invariant pseudo-action formulations. All the fields of the theory depend on the complete extended spacetime. The U-duality group SO(5, 5) is made a geometric symmetry of the theory by virtue of introducing the generalised Lie derivative that incorporates a duality transformation. Tensor hierarchy appears as a natural consequence of the algebra of generalised Lie derivatives that are viewed as gauge transformations. Upon truncating different subsets of the extra coordinates, maximal supergravities in D = 11 and D = 10 (type IIB) can be recovered from this theory.
Quantum Field Theory on a Growing Lattice
Brendan Z. Foster
2005-01-01
We construct the classical and canonically quantized theories of a massless scalar field on a background lattice in which the number of points--and hence the number of modes--may grow in time. To obtain a well-defined theory certain restrictions must be imposed on the lattice. Growth-induced particle creation is studied in a two-dimensional example. The results suggest that local mode birth
Quantum field theory on a growing lattice
Brendan Z. Foster; Ted Jacobson
2004-01-01
We construct the classical and canonically quantized theories of a massless scalar field on a background lattice in which the number of points---and hence the number of modes---may grow in time. To obtain a well-defined theory certain restrictions must be imposed on the lattice. Growth-induced particle creation is studied in a two-dimensional example. The results suggest that local mode birth
Tachyon condensation in superstring field theory
Nathan Berkovits; Ashoke Sen; Barton Zwiebach
2000-01-01
It has been conjectured that at the stationary point of the tachyon potential for the D-brane–anti-D-brane pair or for the non-BPS D-brane of superstring theories, the negative energy density cancels the brane tensions. We study this conjecture using a Wess–Zumino–Witten-like open superstring field theory free of contact term divergences and recently shown to give 60% of the vacuum energy by
Tachyon condensation in string field theory
Ashoke Sen; Barton Zwiebach
2000-01-01
It has been conjectured that at a stationary point of the tachyon potential for the D-brane of bosonic string theory, the negative energy density exactly cancels the D-brane tension. We evaluate this tachyon potential by off-shell calculations in open string field theory. Surprisingly, the condensation of the tachyon mode alone into the stationary point of its cubic potential is found
Quantum Field Theory of Treasury Bonds
Belal E. Baaquie
1998-09-14
The Heath-Jarrow-Morton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM-model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a two-dimensional Gaussian quantum field theory. The no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract.
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.
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.
Quantum field theory based on birefringent modified Maxwell theory
NASA Astrophysics Data System (ADS)
Schreck, M.
2014-04-01
In the current paper the properties of a birefringent Lorentz-violating extension of quantum electrodynamics is considered. The theory results from coupling modified Maxwell theory, which is a CPT-even Lorentz-violating extension of the photon sector, to a Dirac theory of standard spin-1/2 particles. It is then restricted to a special birefringent case with one nonzero Lorentz-violating coefficient. The modified dispersion laws of electromagnetic waves are obtained plus their phase and group velocities are considered. After deriving the photon propagator and the polarization vectors for a special momentum configuration we prove both unitarity at tree level and microcausality for the quantum field theory based on this Lorentz-violating modification. These analytical proofs are done for a spatial momentum with two vanishing components and the proof of unitarity is supported by numerical investigations in case all components are nonvanishing. The upshot is that the theory is well behaved within the framework of our assumptions where there is a possible issue for negative Lorentz-violating coefficients. The paper shall provide a basis for the future analysis of alternative birefringent quantum field theories.
Supergeometry in locally covariant quantum field theory
Thomas-Paul Hack; Florian Hanisch; Alexander Schenkel
2015-01-07
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 --> 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 --> 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.
Supergeometry in locally covariant quantum field theory
Thomas-Paul Hack; Florian Hanisch; Alexander Schenkel
2015-09-16
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 --> 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 --> 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.
Diagrammar in classical scalar field theory
Cattaruzza, E., E-mail: Enrico.Cattaruzza@gmail.com [Department of Physics (Miramare Campus), University of Trieste, Strada Costiera 11, Miramare-Grignano 34014, Trieste (Italy); Gozzi, E., E-mail: gozzi@ts.infn.it [Department of Physics (Miramare Campus), University of Trieste, Strada Costiera 11, Miramare-Grignano 34014, Trieste (Italy); INFN, Sezione di Trieste (Italy); Francisco Neto, A., E-mail: antfrannet@gmail.com [Departamento de Engenharia de Producao, Administracao e Economia, Escola de Minas, Campus Morro do Cruzeiro, UFOP, 35400-000 Ouro Preto MG (Brazil)
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.
Field theory models for tachyon and gauge field string dynamics
Joseph A. Minahan; Barton Zwiebach
2000-09-13
In hep-th/0008227, the unstable lump solution of \\phi^3 theory was shown to have a spectrum governed by the solvable Schroedinger equation with the \\ell=3 reflectionless potential and was used as a model for tachyon condensation in string theory. In this paper we study in detail an \\ell\\to \\infty scalar field theory model whose lump solution mimics remarkably the string theory setup: the original field theory tachyon and the lump tachyon have the same mass, the spectrum of the lump consists of equally spaced infinite levels, there is no continuous spectrum, and nothing survives after tachyon condensation. We also find exact solutions for lumps with codimension \\ge 2, and show that that their tensions satisfy (1/(2\\pi)) (T_p/ T_{p+1})=e/(\\sqrt{2\\pi}) \\approx 1.08. We incorporate gauge fixed couplings to a U(1) gauge field which preserve solvability and result in massless gauge fields on the lump.
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.
A New World Sheet Field Theory
Korkut Bardakci
2008-10-13
A second quantized field theory on the world sheet is developed for summing planar graphs of the phi^3 theory. This is in contrast to the earlier work, which was based on first quantization. The ground state of the model is investigated with the help of a variational ansatz. In complete agreement with standard perturbation theory, the infinities encountered in carrying out this calculation can be eliminated by the renormalization of the parameters of the model. We also find that, as in the earlier work, in the ground state, graphs form a dense network (condensate) on the world sheet.
On the theory of a non-linear neutral scalar field with spontaneously broken symmetry
Y. M. Poluektov
2015-07-08
On the example of a real scalar field, an approach to quantization of non-linear fields and construction of the perturbation theory with account of spontaneous symmetry breaking is proposed. The method is based on using as the main approximation of the relativistic self-consistent field model, in which the influence of vacuum field fluctuations is taken into account when constructing the one-particle states. The solutions of the self-consistent equations determine possible states, which also include the states with broken symmetries. Different states of the field are matched to particles, whose masses are determined by both parameters of the Lagrangian and vacuum fluctuations. The density of the vacuum energy in these states is calculated. It is shown that the concept of Bogolubov's quasi-averages can naturally be applied for definition of exact Green functions in the states with broken symmetries. Equations for exact one- and two-point Green functions are obtained.
New approach to vacuum string field theory
NASA Astrophysics Data System (ADS)
Zeze, S.
2014-06-01
We discuss the possibility of applying a purely ghost kinetic operator in open string field theory from the perspective of a modern analytic method based on the KBc subalgebra. A purely ghost kinetic operator is obtained as a result of gauge fixing string field theory around the identity-based tachyon vacuum solution. We show that the obtained kinetic operator is not equivalent to the midpoint insertion of a conformal ghost, to which an extensive literature is devoted. We also show that the equation of motion does not admit nontrivial solutions.
Recent progress in irrational conformal field theory
Halpern, M.B.
1993-09-01
In this talk, I will review the foundations of irrational conformal field theory (ICFT), which includes rational conformal field theory as a small subspace. Highlights of the review include the Virasoro master equation, the Ward identities for the correlators of ICFT and solutions of the Ward identities. In particular, I will discuss the solutions for the correlators of the g/h coset construction and the correlators of the affine-Sugawara nests on g {contains} h{sub 1} {contains} {hor_ellipsis} {contains} h{sub n}. Finally, I will discuss the recent global solution for the correlators of all the ICFT`s in the master equation.
Quantization of n coupled scalar field theory
NASA Astrophysics Data System (ADS)
Kim, Yong-Wan; Myung, Yun Soo; Park, Young-Jai
2013-10-01
We study a model of n coupled scalar fields in Minkowski spacetime in which all masses degenerate, which is considered as a toy model of polycritical gravity on anti-de Sitter spacetime. We quantize this model within the Becchi-Rouet-Stora-Tyutin scheme by introducing n Faddeev-Popov (FP) ghost fields. Extending a Becchi-Rouet-Stora-Tyutin quartet generated by two scalars and two FP ghosts to n scalars and n FP ghosts, there remains a physical subspace with positive norm for odd n, but there exists only the vacuum for even n. This clearly shows a nontriviality of odd higher-order derivative scalar field theories. This is helpful to understand the truncation mechanism, which is used to obtain a unitary conformal field theory dual to linearized polycritical gravity. It turns out that the truncation mechanism is nothing but a general quartet mechanism that appears when introducing the FP ghost action.
A new look at electromagnetic field theory
Mendel Sachs
1980-01-01
The most general expression of electromagnetic theory is examined in the light of (1) Faraday's interpretation of the field\\u000a as a potentiality for the force of charged matter to act upon a test body, and (2) Einstein's view of the field equations\\u000a as an example of a covariant expression of special relativity. Faraday's original interpretation, in which all physical variables
Super-Poincaré invariant superstring field theory
Nathan Berkovits
1995-01-01
Using the topological techniques developed in an earlier paper with Vafa, a field theory action is constructed for any open string with critical N = 2 worldsheet superconformal invariance. Instead of the Chem-Simons-like action found by Witten, this action resembles that of a Wess-Zumino-Witten model. For the N = 2 string which describes (2,2) self-dual Yang-Mills, the string field generalizes
Aspects of locally covariant quantum field theory
Ko Sanders
2008-09-28
This thesis considers various aspects of locally covariant quantum field theory (LCQFT; see Brunetti et al., Commun.Math.Phys. 237 (2003), 31-68), a mathematical framework to describe axiomatic quantum field theories in curved spacetimes. New results include: a philosophical interpretation of certain aspects of this framework in terms of modal logic; a proof that the truncated n-point functions of any Hadamard state of the free real scalar field are smooth, except for n=2; a description of he free Dirac field in a representation independent way, showing that the theory is determined entirely by the relations between the adjoint map, the charge conjugation map and the Dirac operator; a proof that the relative Cauchy evolution of the free Dirac field is related to its stress-energy-momentum tensor in the same way as for the free real scalar field (cf. loc.cit.); several results on the Reeh-Schlieder property in LCQFT, including but not limited to those of our earlier paper; a new and elegant approach to wave front sets of Banach space-valued distributions, which allows easy proofs and extensions of results in the literature.
On quantum field theory with invariant parameter
NASA Astrophysics Data System (ADS)
Hannibal, Ludger
1994-12-01
The Dirac-type quantum theory with invariant parameter is formulated in a way such that for particle states with positive frequencies and antiparticle states with negative frequencies the energy densities and probability densities all are positive. This consistent formulation of single-particle quantum theory for spin-1/2 is used as a basis for second quantization. The inclusion of an invariant parameter into quantum field theory leads us to describe antiparticles by states with negative frequencies. The correct signs for all physical quantities are achieved by a unified definition of mass, charge, and energy-momentum density operators as infinitesimal generators of the corresponding symmetries, of translations of the invariant parameter, U(1)-gauge transformations, and space-time translations, respectively. A quantum field theory of massive free spin-1/2 and spin-0 fields is obtained with antiunitary charge conjugation transformation and unitary CPT transformation. The theory has a new discrete symmetry transformation which is interesting for the description of weak interactions.
Continuous wavelet transform in quantum field theory
NASA Astrophysics Data System (ADS)
Altaisky, M. V.; Kaputkina, N. E.
2013-07-01
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ?4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ?4 theory, consists in substitution of the local fields ?(x) by those dependent on both the position x and the resolution a. The substitution of the action S[?(x)] by the action S[?a(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=??a1(x1)…?an(xn)? finite for any given set of regions by means of an effective cutoff scale A=min?(a1,…,an).
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.
Analogue gravity from field theory normal modes?
Carlos Barceló; Stefano Liberati; Matt Visser
2001-01-01
We demonstrate that the emergence of a curved spacetime `effective Lorentzian geometry' is a common and generic result of linearizing a classical scalar field theory around some non-trivial background configuration. This investigation is motivated by considering the large number of `analogue models' of general relativity that have recently been developed based on condensed matter physics, and asking whether there is
Recent Progress in Group Field Theory
Oriti, Daniele [Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Muehlenberg 1 D-14476 Golm (Germany)
2009-12-15
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical definition of these models, and possible avenues towards extracting interesting physics from them.
Superconformal field theory and operator algebras
Sunder, V S
, the stress-energy tensor, and G(z) = rZ+1/2 Grz-r-3/2 , the super stress-energy tensor. These power series, August 2010 Yasu Kawahigashi (Univ. Tokyo) Super CFT and operator algebras Chennai, August 2010 1 / 15 #12;Quantum field theory and von Neumann algebras Outline of the talk: 1 N = 1 Super Virasoro algebras
Feynman graphs in perturbative quantum field theory
Christian Bogner; Stefan Weinzierl
2009-12-22
In this talk we discuss mathematical structures associated to Feynman graphs. Feynman graphs are the backbone of calculations in perturbative quantum field theory. The mathematical structures -- apart from being of interest in their own right -- allow to derive algorithms for the computation of these graphs. Topics covered are the relations of Feynman integrals to periods, shuffle algebras and multiple polylogarithms.
Progress in Lattice Field Theory Algorithms
A. D. Kennedy
1992-12-14
I present a summary of recent algorithmic developments for lattice field theories. In particular I give a pedagogical introduction to the new Multicanonical algorithm, and discuss the relation between the Hybrid Overrelaxation and Hybrid Monte Carlo algorithms. I also attempt to clarify the role of the dynamical critical exponent z and its connection with `computational cost.' [Includes four PostScript figures
Gauge Dressing of 2D Field Theories
Ian I. Kogan; Alex Lewis; Oleg A. Soloviev
1996-07-05
By using the gauge Ward identities, we study correlation functions of gauged WZNW models. We show that the gauge dressing of the correlation functions can be taken into account as a solution of the Knizhnik-Zamolodchikov equation. Our method is analogous to the analysis of the gravitational dressing of 2D field theories.
Electromagnetic interactions in Halo Effective Field Theory
Renato Higa
2010-01-04
After a brief discussion of effective field theory applied to nuclear clusters, I concentrate on the inclusion of two particular aspects, namely, narrow resonances and electromagnetic interactions. As examples of applications, I present the details of our studies on alpha-alpha and proton-alpha scattering.
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.
Strongly Coupled Chameleon Fields: New Horizons in Scalar Field Theory
David F. Mota; Douglas J. Shaw
2006-09-16
We show that as a result of non-linear self-interactions, scalar field theories that couple to matter much more strongly than gravity are not only viable but could well be detected by a number of future experiments, provided these are properly designed to do so.
Logarithmic conformal field theory: beyond an introduction
NASA Astrophysics Data System (ADS)
Creutzig, Thomas; Ridout, David
2013-12-01
This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with the remarkable observation of Cardy that the horizontal crossing probability of critical percolation may be computed analytically within the formalism of boundary conformal field theory. Cardy’s derivation relies on certain implicit assumptions which are shown to lead inexorably to indecomposable modules and logarithmic singularities in correlators. For this, a short introduction to the fusion algorithm of Nahm, Gaberdiel and Kausch is provided. While the percolation logarithmic conformal field theory is still not completely understood, there are several examples for which the formalism familiar from rational conformal field theory, including bulk partition functions, correlation functions, modular transformations, fusion rules and the Verlinde formula, has been successfully generalized. This is illustrated for three examples: the singlet model \\mathfrak {M} (1,2), related to the triplet model \\mathfrak {W} (1,2), symplectic fermions and the fermionic bc ghost system; the fractional level Wess-Zumino-Witten model based on \\widehat{\\mathfrak {sl}} \\left( 2 \\right) at k=-\\frac{1}{2}, related to the bosonic ?? ghost system; and the Wess-Zumino-Witten model for the Lie supergroup \\mathsf {GL} \\left( 1 {\\mid} 1 \\right), related to \\mathsf {SL} \\left( 2 {\\mid} 1 \\right) at k=-\\frac{1}{2} and 1, the Bershadsky-Polyakov algebra W_3^{(2)} and the Feigin-Semikhatov algebras W_n^{(2)}. These examples have been chosen because they represent the most accessible, and most useful, members of the three best-understood families of logarithmic conformal field theories. The logarithmic minimal models \\mathfrak {W} (q,p), the fractional level Wess-Zumino-Witten models, and the Wess-Zumino-Witten models on Lie supergroups (excluding \\mathsf {OSP} \\left( 1 {\\mid} 2n \\right)). In this review, the emphasis lies on the representation theory of the underlying chiral algebra and the modular data pertaining to the characters of the representations. Each of the archetypal logarithmic conformal field theories is studied here by first determining its irreducible spectrum, which turns out to be continuous, as well as a selection of natural reducible, but indecomposable, modules. This is followed by a detailed description of how to obtain character formulae for each irreducible, a derivation of the action of the modular group on the characters, and an application of the Verlinde formula to compute the Grothendieck fusion rules. In each case, the (genuine) fusion rules are known, so comparisons can be made and favourable conclusions drawn. In addition, each example admits an infinite set of simple currents, hence extended symmetry algebras may be constructed and a series of bulk modular invariants computed. The spectrum of such an extended theory is typically discrete and this is how the triplet model \\mathfrak {W} (1,2) arises, for example. Moreover, simple current technology admits a derivation of the extended algebra fusion rules from those of its continuous parent theory. Finally, each example is concluded by a brief description of the computation of some bulk correlators, a discussion of the structure of the bulk state space, and remarks concerning more advanced developments and generalizations. The final part gives a very short account of the theory of staggered modules, the (simplest class of) representations that are responsible for the logarithmic singularities that distinguish logarithmic theories from their rational cousins. These modules are discussed in a generality suitable to encompass all the examples met in this review and some of the very basic structure theory is proven. Then, the important quantities known as logarithmic couplings are reviewed for Virasoro staggered modules and their role as fundamentally important parameters, akin to the three-point constants of rational conformal field theory, is discussed. An appendix is also provided in order to introduce some of the necessary, but perhaps unfamiliar, la
Shape Dynamics and Effective Field Theory
NASA Astrophysics Data System (ADS)
Koslowski, Tim A.
2013-05-01
Shape dynamics is a gauge theory based on spatial diffeomorphism- and Weyl-invariance which is locally indistinguishable from classical general relativity. If taken seriously, it suggests that the space-time geometry picture that underlies general relativity can be replaced by a picture based on spatial conformal geometry. This classically well-understood trading of gauge symmetries opens new conceptual avenues in many approaches to quantum gravity. This paper focusses on the general implications for quantum gravity and effective field theory and considers the application of the shape dynamics picture in the exact renormalization group approaches to gravity, loop- and polymer-quantization approaches to gravity and low energy effective field theories. Also, the interpretation of known results is discussed through the shape dynamics picture, particularly holographic renormalization and the problem of time in canonical quantum gravity.
Effective Field Theory for Bound State Reflection
Michelle Pine; Dean Lee
2013-01-17
Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory for elastic reflection of shallow dimers from hard-wall surfaces using effective field theory. We show that there is a small expansion parameter for analytic calculations of the reflection scattering length. We present a calculation up to second order in the effective Hamiltonian in one, two, and three dimensions. We also provide numerical lattice results for all three cases as a comparison with our effective field theory results. Finally, we provide an analysis of the compressibility of the alpha particle confined to a cubic lattice with vanishing Dirichlet boundaries.
Lagrangian crumpling equations.
Peterson, Mark A
2009-08-01
A concise method for following the evolving geometry of a moving surface using Lagrangian coordinates is described. All computations can be done in the fixed geometry of the initial surface despite the evolving complexity of the moving surface. The method is applied to three problems in nonlinear elasticity: the bulging of a thin plate under pressure (the original motivation for Föppl-von Karman theory), the buckling of a spherical shell under pressure, and the phenomenon of capillary wrinkles induced by surface tension in a thin film. In this last problem the inclusion of a gravitational potential-energy term in the total energy improves the agreement with experiment. PMID:19792134
Weighting bubbles in group field theory
NASA Astrophysics Data System (ADS)
Baratin, Aristide; Freidel, Laurent; Gurau, Razvan
2014-07-01
Group field theories (GFT) are higher dimensional generalizations of matrix models whose Feynman diagrams are dual to triangulations. Here we propose a modification of GFT models that includes extra field indices keeping track of the bubbles of the graphs in the Feynman evaluations. In dimension three, our model exhibits new symmetries, interpreted as the action of the vertex translations of the triangulation. The extra field indices have an elegant algebraic interpretation: they encode the structure of a semisimple algebra. Remarkably, when the algebra is chosen to be associative, the new structure contributes a topological invariant from each bubble of the graph to the Feynman amplitudes.
Weighting bubbles in group field theory
Aristide Baratin; Laurent Freidel; Razvan Gurau
2014-06-20
Group field theories (GFT) are higher dimensional generalizations of matrix models whose Feynman diagrams are dual to triangulations. Here we propose a modification of GFT models that includes extra field indices keeping track of the bubbles of the graphs in the Feynman evaluations. In dimension three, our model exhibits new symmetries, interpreted as the action of the vertex translations of the triangulation. The extra field indices have an elegant algebraic interpretation: they encode the structure of a semi-simple algebra. Remarkably, when the algebra is chosen to be associative, the new structure contributes a topological invariant from each bubble of the graph to the Feynman amplitudes.
Spectral density constraints in quantum field theory
Peter Lowdon
2015-04-02
Determining the structure of spectral densities is important for understanding the behaviour of any quantum field theory (QFT). However, the exact calculation of these quantities often requires a full non-perturbative description of the theory, which for physically realistic theories such as Quantum Chromodynamics (QCD) is currently unknown. Nevertheless, it is possible to infer indirect information about these quantities. In this paper we demonstrate an approach for constraining the form of spectral densities associated with QFT propagators, which involves matching the short distance expansion of the spectral representation with the operator product expansion (OPE) of the propagators. As an application of this procedure we analyse the scalar propagator in $\\phi^4$-theory and the quark propagator in QCD, and show that constraints are obtained both on the spectral densities and the OPE condensates.
Symmetry aspects of nonholonomic field theories
J. Vankerschaver; D. Martin de Diego
2007-12-14
The developments in this paper are concerned with nonholonomic field theories in the presence of symmetries. Having previously treated the case of vertical symmetries, we now deal with the case where the symmetry action can also have a horizontal component. As a first step in this direction, we derive a new and convenient form of the field equations of a nonholonomic field theory. Nonholonomic symmetries are then introduced as symmetry generators whose virtual work is zero along the constraint submanifold, and we show that for every such symmetry, there exists a so-called momentum equation, describing the evolution of the associated component of the momentum map. Keeping up with the underlying geometric philosophy, a small modification of the derivation of the momentum lemma allows us to treat also generalized nonholonomic symmetries, which are vector fields along a projection. Such symmetries arise for example in practical examples of nonholonomic field theories such as the Cosserat rod, for which we recover both energy conservation (a previously known result), as well as a modified conservation law associated with spatial translations.
An Effective Field Theory for Jet Processes
Becher, Thomas; Rothen, Lorena; Shao, Ding Yu
2015-01-01
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 momentum modes which 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 fully separates the physics at different energy scales. Solving its renormalization-group equations resums all logarithmically enhanced higher-order terms in cone-jet processes, in particular also the non-global logarithms.
An Effective Field Theory for Jet Processes
Thomas Becher; Matthias Neubert; Lorena Rothen; Ding Yu Shao
2015-08-26
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 momentum modes which 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 fully separates the physics at different energy scales. Solving its renormalization-group equations resums all logarithmically enhanced higher-order terms in cone-jet processes, in particular also the non-global 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(?/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
Field Theory for Zero Sound and Ion Acoustic Wave in Astrophysical Matter
Gregory Gabadadze; Rachel A Rosen
2015-07-24
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 point-like 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 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.
Field Theory for Zero Sound and Ion Acoustic Wave in Astrophysical Matter
Gabadadze, Gregory
2015-01-01
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 point-like 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 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.
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.
A master functional for quantum field theory
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2013-04-01
We study a new generating functional of one-particle irreducible diagrams in quantum field theory, called master functional, which is invariant under the most general perturbative changes of field variables. The usual functional ? does not behave as a scalar under the transformation law inherited from its very definition as the Legendre transform of W=ln Z, although it does behave as a scalar under an unusual transformation law. The master functional, on the other hand, is the Legendre transform of an improved functional W with respect to the sources coupled to both elementary and composite fields. The inclusion of certain improvement terms in W and Z is necessary to make this new Legendre transform well defined. The master functional behaves as a scalar under the transformation law inherited from its very definition. Moreover, it admits a proper formulation, obtained extending the set of integrated fields to so-called proper fields, which allows us to work without passing through Z, W or ?. In the proper formulation the classical action coincides with the classical limit of the master functional, and correlation functions and renormalization are calculated applying the usual diagrammatic rules to the proper fields. Finally, the most general change of field variables, including the map relating bare and renormalized fields, is a linear redefinition of the proper fields.
Tachyon Vacuum in Cubic Superstring Field Theory
Theodore Erler
2007-07-31
In this paper we give an exact analytic solution for tachyon condensation in the modified (picture 0) cubic superstring field theory. We prove the absence of cohomology and, crucially, reproduce the correct value for the D-brane tension. The solution is surprising for two reasons: First, the existence of a tachyon vacuum in this theory has not been definitively established in the level expansion. Second, the solution {\\it vanishes} in the GSO$(-)$ sector, implying a ``tachyon vacuum'' solution exists even for a {\\it BPS} D-brane.
Tachyon condensation in string field theory
Ashoke Sen; Barton Zwiebach
1999-12-24
It has been conjectured that at a stationary point of the tachyon potential for the D-brane of bosonic string theory, the negative energy density exactly cancels the D-brane tension. We evaluate this tachyon potential by off-shell calculations in open string field theory. Surprisingly, the condensation of the tachyon mode alone into the stationary point of its cubic potential is found to cancel about 70% of the D-brane tension. Keeping relevant scalars up to four mass levels above the tachyon, the energy density at the shifted stationary point cancels 99% of the D-brane tension.
Hydrodynamic flow structures in quantum field theory
Carruthers, P.; Zachariasen, F.
1984-05-01
The transport of matter is examined in the context of relativistic quantum transport theory for the case of neutral scalar fields. The goal is to formulate a theory valid off mass shell and out of equilibrium. We construct a conserved moment tensor which coincides with the ensemble average of the Noether tensor, or the improved energy-momentum tensor within an additive constant of the improvement term. Conditions for closure of the conservation equation are given for the phi/sup 4/ coupling. 8 references.
String Field Theory from Quantum Gravity
Louis Crane
2012-01-02
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 $E_6$, 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.
Fields and Galois Theory Version 4.21
Gavarini, Fabio
Fields and Galois Theory J.S. Milne Version 4.21 September 28, 2008 #12;These notes give a concise exposition of the theory of fields, including the Galois theory of finite and infinite extensions={Fields and Galois Theory (v4.21)}, year={2008}, note={Available at www.jmilne.org/math/}, pages={107+iv} } v2
Frobenius Algebra Structures in Topological Quantum Field Theory
Abrams, Lowell
Frobenius Algebra Structures in Topological Quantum Field Theory and Quantum Cohomology by Lowell on this, we prove the oneÂtoÂone correspondence between topological quantum field theories and Frobenius and Number Theory . . . . . . . . . . . 31 3 Topological Quantum Field Theories 37 3.1 Two
Undergraduate Lecture Notes in Topological Quantum Field Theory
Vladimir G. Ivancevic; Tijana T. Ivancevic
2008-12-11
These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism. Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory
Noether symmetries, energy-momentum tensors, and conformal invariance in classical field theory
Pons, Josep M. [Departament ECM and ICC, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia (Spain)
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.
Leonardo Modesto
2004-01-04
In this paper we work in perturbative Quantum Gravity coupled to Scalar Matter at tree level and we introduce a new effective model in analogy with the Fermi theory of weak interaction and in relation with a previous work where we have studied only the gravity and its self-interaction. This is an extension of the I.T.B model (Intermediate-Tensor-Boson) for gravity also to gravitational interacting scalar matter. We show that in a particular gauge the infinite series of interactions containing "n" gravitons and two scalars could be rewritten in terms of only two Lagrangians containing a massive field, the graviton and, obviously, the scalar field. Using the S-matrix we obtain that the low energy limit of the amplitude reproduce the local Lagrangian for the scalar matter coupled to gravity.
Complete action of open superstring field theory
Kunitomo, Hiroshi
2015-01-01
We construct a complete action of open superstring field theory which 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, we use the string field in the small Hilbert space which is further projected to a subspace so that the BRST cohomology on the subspace reproduces the correct spectrum. We show that the action is invariant under gauge transformations which are consistent with the projection for the string field in the Ramond sector.
Advances in mean-field dynamo theories
NASA Astrophysics Data System (ADS)
Pipin, V. V.
2013-07-01
We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean electromotive force of the turbulent flows and magnetic field, the nonlinear effects of the magnetic helicity, the non-local generation effects in the dynamo. We give an example of the mean-field solar dynamo model that incorporates the fairly complete expressions for the mean-electromotive force, the subsurface shear layer and the conservation of the total helicity. The model is used to shed light on the issues in the solar dynamo and on the future development of this field of research.
Nuclear effective field theory on the lattice
Hermann Krebs; Bugra Borasoy; Evgeny Epelbaum; Dean Lee; Ulf-G. Meiß ner
2008-10-01
In the low-energy region far below the chiral symmetry breaking scale (which is of the order of 1 GeV) chiral perturbation theory provides a model-independent approach for quantitative description of nuclear processes. In the two- and more-nucleon sector perturbation theory is applicable only at the level of an effective potential which serves as input in the corresponding dynamical equation. To deal with the resulting many-body problem we put chiral effective field theory (EFT) on the lattice. Here we present the results of our lattice EFT study up to next-to-next-to-leading order in the chiral expansion. Accurate description of two-nucleon phase-shifts and ground state energy ratio of dilute neutron matter up to corrections of higher orders shows that lattice EFT is a promising tool for a quantitative description of low-energy few- and many-body systems.
Graphene as a Lattice Field Theory
Simon Hands; Wes Armour; Costas Strouthos
2015-01-08
We introduce effective field theories for the electronic properties of graphene in terms of relativistic fermions propagating in 2+1 dimensions, and outline how strong inter-electron interactions may be modelled by numerical simulation of a lattice field theory. For strong enough coupling an insulating state can form via condensation of particle-hole pairs, and it is demonstrated that this is a theoretical possibility for monolayer graphene. For bilayer graphene the effect of an interlayer bias voltage can be modelled by the introduction of a chemical potential (akin to isopsin chemical potential in QCD) with no accompanying sign problem; simulations reveal the presence of strong interactions among the residual degrees of freedom at the resulting Fermi surface, which is disrupted by an excitonic condensate. We also present preliminary results for the quasiparticle dispersion, which permit direct estimates of both the Fermi momentum and the induced gap.
Graphene as a Lattice Field Theory
Hands, Simon; Strouthos, Costas
2015-01-01
We introduce effective field theories for the electronic properties of graphene in terms of relativistic fermions propagating in 2+1 dimensions, and outline how strong inter-electron interactions may be modelled by numerical simulation of a lattice field theory. For strong enough coupling an insulating state can form via condensation of particle-hole pairs, and it is demonstrated that this is a theoretical possibility for monolayer graphene. For bilayer graphene the effect of an interlayer bias voltage can be modelled by the introduction of a chemical potential (akin to isopsin chemical potential in QCD) with no accompanying sign problem; simulations reveal the presence of strong interactions among the residual degrees of freedom at the resulting Fermi surface, which is disrupted by an excitonic condensate. We also present preliminary results for the quasiparticle dispersion, which permit direct estimates of both the Fermi momentum and the induced gap.
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.
Quantum field theory of relic nonequilibrium systems
NASA Astrophysics Data System (ADS)
Underwood, Nicolas G.; Valentini, Antony
2015-09-01
In terms of the de Broglie-Bohm pilot-wave formulation of quantum theory, we develop field-theoretical models of quantum nonequilibrium systems which could exist today as relics from the very early Universe. We consider relic excited states generated by inflaton decay, as well as relic vacuum modes, for particle species that decoupled close to the Planck temperature. Simple estimates suggest that, at least in principle, quantum nonequilibrium could survive to the present day for some relic systems. The main focus of this paper is to describe the behavior of such systems in terms of field theory, with the aim of understanding how relic quantum nonequilibrium might manifest experimentally. We show by explicit calculation that simple perturbative couplings will transfer quantum nonequilibrium from one field to another (for example from the inflaton field to its decay products). We also show that fields in a state of quantum nonequilibrium will generate anomalous spectra for standard energy measurements. Possible connections to current astrophysical observations are briefly addressed.
Cosmological tachyon from cubic string field theory
Gianluca Calcagni
2006-05-04
The classical dynamics of the tachyon scalar field of cubic string field theory is considered on a cosmological background. Starting from a nonlocal action with arbitrary tachyon potential, which encodes the bosonic and several supersymmetric cases, we study the equations of motion in the Hamilton-Jacobi formalism and with a generalized Friedmann equation, appliable in braneworld or modified gravity models. The cases of cubic (bosonic) and quartic (supersymmetric) tachyon potential in general relativity are automatically included. We comment the validity of the slow-roll approximation, the stability of the cosmological perturbations, and the relation between this tachyon and the Dirac-Born-Infeld one.
Massive Type II in Double Field Theory
Olaf Hohm; Seung Ki Kwak
2011-08-24
We provide an extension of the recently constructed double field theory formulation of the low-energy limits of type II strings, in which the RR fields can depend simultaneously on the 10-dimensional space-time coordinates and linearly on the dual winding coordinates. For the special case that only the RR one-form of type IIA carries such a dependence, we obtain the massive deformation of type IIA supergravity due to Romans. For T-dual configurations we obtain a `massive' but non-covariant formulation of type IIB, in which the 10-dimensional diffeomorphism symmetry is deformed by the mass parameter.
Nonperturbative renormalization of effective field theory
Yang, J -F
2009-01-01
Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of $T$-matrices are unraveled using rigorous solutions and an inverse form of algebraic Lippmann-schwinger equation. The intrinsic mismatches between effective field theory power counting and nonperturbative divergence structures are shown for the first time to preclude the conventional counterterm algorithm from working in the renormalization of EFT for $NN$ scattering in nonperturbative regimes.
Tachyon condensation in cubic superstring field theory
I. Ya. Aref'eva; A. S. Koshelev; D. M. Belov; P. B. Medvedev
2002-01-01
It has been conjectured that at the stationary point of the tachyon potential for the non-BPS D-brane or brane–anti-D-brane pair, the negative energy density cancels the brane tension. We study this conjecture using a cubic superstring field theory with insertion of a double-step inverse picture changing operator. We compute the tachyon potential at levels (1\\/2,1) and (2,6). In the first
Advances in String Field Theory (Abstract)
Schnabl, M. [Institute of Advanced Study, Princeton, NJ 08540 (United States)
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.
Non-compact WZW conformal field theories
Krzysztof Gawedzki
1991-01-01
Non-compact WZW sigma models are considered, especially the ones with symmetric space H(sup C)\\/H as the target, for H in a compact Lie group. The author offers examples of non-rational conformal field theories. The author notes their relation to the compact WZW models, but stresses their distinctive features such as the continuous spectrum of conformal weights, diverging partition functions, and
Fundamentals of nonassociative classical field theory
Kurdgelaidze, D.F.
1987-05-01
A nonassociative classical field theory is constructed. Octonion algebra is studied. The octonion is represented as the sum of a quaternion and an associator. The octonion algebra is expanded and Lorentz group generators are specified in terms of octonion bases in one of the subalgebras. Lorentz vectors and spinors are constructed in the nonassociative algebra. The representation of the Lorentz group in terms of spin and the associator is obtained.
Loop quantum cosmology from group field theory
Gianluca Calcagni
2014-09-27
We show that the effective dynamics of the recently proposed isotropic condensate state of group field theory with Laplacian kinetic operator can be equivalent to that of homogeneous and isotropic loop quantum cosmology in the improved dynamics quantization scheme, where the area of elementary holonomy plaquettes is constant. This constitutes a somewhat surprising example of a cosmological model of quantum gravity where the operations of minisuperspace symmetry reduction and quantization can actually commute.
Some boundary effects in quantum field theory
Bezerra, V.B.; Rego-Monteiro, M.A. [Departamento de Fisica, Universidade Federal da Paraiba, Caixa Postal 5008, 58051-970 Joao Pessoa, PB (Brazil); Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ (Brazil)
2004-09-15
We have constructed a quantum field theory in a finite box, with periodic boundary conditions, using the hypothesis that particles living in a finite box are created and/or annihilated by the creation and/or annihilation operators, respectively, of a quantum harmonic oscillator on a circle. An expression for the effective coupling constant is obtained, showing explicitly its dependence on the dimension of the box.
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.
Locality in Free String Field Theory II. J. Dimock #
Locality in Free String Field Theory Â II. J. Dimock # Dept. of Mathematics SUNY at Bu#alo Bu#alo, NY 14214 January 29, 2001 Abstract We study the covariant free bosonic string field theory field theory 14 3.1 String field equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3
The flux-rope-fibre theory of solar magnetic fields
J. H. Piddington
1978-01-01
The flux-rope theory of solar magnetic fields is reviewed briefly and, together with the dynamo theory, compared with various observational results. Dynamo and related theories are based on fields controlled by the plasma, and it is shown that such fields cannot account for the strong surface fields or even emerge without becoming tangled. Observations which appear uniquely explicable in terms
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.
Non-Compact WZW Conformal Field Theories
Krzysztof Gawedzki
1991-10-31
We discuss non-compact WZW sigma models, especially the ones with symmetric space $H^{\\bf C}/H$ as the target, for $H$ a compact Lie group. They offer examples of non-rational conformal field theories. We remind their relation to the compact WZW models but stress their distinctive features like the continuous spectrum of conformal weights, diverging partition functions and the presence of two types of operators analogous to the local and non-local insertions recently discussed in the Liouville theory. Gauging non-compact abelian subgroups of $H^{\\bf C}$ leads to non-rational coset theories. In particular, gauging one-parameter boosts in the $SL(2,\\bC)/SU(2)$ model gives an alternative, explicitly stable construction of a conformal sigma model with the euclidean 2D black hole target. We compute the (regularized) toroidal partition function and discuss the spectrum of the theory. A comparison is made with more standard approach based on the $U(1)$ coset of the $SU(1,1)$ WZW theory where stability is not evident but where unitarity becomes more transparent.
Noisy Lagrangian Tracers for Filtering Random Rotating Compressible Flows
NASA Astrophysics Data System (ADS)
Chen, Nan; Majda, Andrew J.; Tong, Xin T.
2015-06-01
The recovery of a random turbulent velocity field using Lagrangian tracers that move with the fluid flow is a practically important problem. This paper studies the filtering skill of -noisy Lagrangian tracers in recovering random rotating compressible flows that are a linear combination of random incompressible geostrophically balanced (GB) flow and random rotating compressible gravity waves. The idealized random fields are defined through forced damped random amplitudes of Fourier eigenmodes of the rotating shallow-water equations with the rotation rate measured by the Rossby number . In many realistic geophysical flows, there is fast rotation so satisfies and the random rotating shallow-water equations become a slow-fast system where often the primary practical objective is the recovery of the GB component from the Lagrangian tracer observations. Unfortunately, the -noisy Lagrangian tracer observations are highly nonlinear and mix the slow GB modes and the fast gravity modes. Despite this inherent nonlinearity, it is shown here that there are closed analytical formulas for the optimal filter for recovering these random rotating compressible flows for any involving Ricatti equations with random coefficients. The performance of the optimal filter is compared and contrasted through mathematical theorems and concise numerical experiments with the performance of the optimal filter for the incompressible GB random flow with -noisy Lagrangian tracers involving only the GB part of the flow. In addition, a sub-optimal filter is defined for recovering the GB flow alone through observing the -noisy random compressible Lagrangian trajectories, so the effect of the gravity wave dynamics is unresolved but effects the tracer observations. Rigorous theorems proved below through suitable stochastic fast-wave averaging techniques and explicit formulas rigorously demonstrate that all these filters have comparable skill in recovering the slow GB flow in the limit for any bounded time interval. Concise numerical experiments confirm the mathematical theory and elucidate various new features of filter performance as the Rossby number , the number of tracers and the tracer noise variance change.
Galvao, C.A. [Universidade de Brasilia, Departamento de Fisica, 70.910 Brasilia DF, (Brasil)] [Universidade de Brasilia, Departamento de Fisica, 70.910 Brasilia DF, (Brasil); Nutku, Y. [TUeBITAK---Marmara Research Center, Research Institute for Basic Sciences, Department of Physics, 41470 Gebze (Turkey)] [TUeBITAK---Marmara Research Center, Research Institute for Basic Sciences, Department of Physics, 41470 Gebze (Turkey)
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.}
Analog gravity from field theory normal modes?
Carlos Barcelo; Stefano Liberati; Matt Visser
2001-04-02
We demonstrate that the emergence of a curved spacetime ``effective Lorentzian geometry'' is a common and generic result of linearizing a field theory around some non-trivial background. This investigation is motivated by considering the large number of ``analog models'' of general relativity that have recently been developed based on condensed matter physics, and asking whether there is something more fundamental going on. Indeed, linearization of a classical field theory (a field theoretic ``normal mode analysis'') results in fluctuations whose propagation is governed by a Lorentzian-signature curved spacetime ``effective metric''. For a single scalar field, this procedure results in a unique effective metric, which is quite sufficient for simulating kinematic aspects of general relativity (up to and including Hawking radiation). Quantizing the linearized fluctuations, the one-loop effective action contains a term proportional to the Einstein--Hilbert action, suggesting that while classical physics is responsible for generating an ``effective geometry'', quantum physics can be argued to induce an ``effective dynamics''. The situation is strongly reminiscent of Sakharov's ``induced gravity'' scenario, and suggests that Einstein gravity is an emergent low-energy long-distance phenomenon that is insensitive to the details of the high-energy short-distance physics. (We mean this in the same sense that hydrodynamics is a long-distance emergent phenomenon, many of whose predictions are insensitive to the short-distance cutoff implicit in molecular dynamics.)
Quantum fields in curved spaces: Kinetic theory
Habib, S.
1988-01-01
The extension of flat space quantum kinetic theory to curved space-times is described. This is accomplished by implementing a generalized Wigner transformation on the Hadamard function of the field theory. A quasilocal momentum space is introduced via Riemann normal coordinates. An exact treatment of the field in purely kinetic terms is impossible; off-shell behavior is accounted for, to some degree, by the introduction of an expansion around the mass-shell. In curved spacetime, free scalar and spinor fields are considered. It is shown that the Wigner transformation leads to quantum corrected Einstein-Vlasov equations having the expected classical limits. The stress tensor for a free scalar field is constructed in terms of the Wigner function. Divergences are isolated by dimensional regularization and covariant conservation is demonstrated. A model of time-dependent oscillators is considered. The oscillators have time dependent frequencies and interactions. An exact Langevin equation for the system is derived. The model is then studied in a settling appropriate for de Sitter space. Two new effects are found: (1) a time dependent contribution to the effective potential with indeterminate sign and (2) a noise-dependent viscosity.
Transfer operators and topological field theory
Igor V. Ovchinnikov
2015-08-20
The transfer operator (TO) formalism of the dynamical systems (DS) theory is reformulated here in terms of the recently proposed supersymetric theory of stochastic differential equations (SDE). It turns out that the stochastically generalized TO (GTO) of the DS theory is the finite-time Fokker-Planck evolution operator. As a result comes the supersymmetric trivialization of the so-called sharp trace and sharp determinant of the GTO, with the former being the Witten index, which is also the stochastic generalization of the Lefschetz index so that it equals the Euler characteristic of the (closed) phase space for any flow vector field, noise metric, and temperature. The enabled possibility to apply the spectral theorems of the DS theory to the Fokker-Planck operators allows to extend the previous picture of the spontaneous topological supersymmetry (Q-symmetry) breaking onto the situations with negative ground state's attenuation rate. The later signifies the exponential growth of the number of periodic solutions/orbits in the large time limit, which is the unique feature of chaotic behavior proving that the spontaneous breakdown of Q-symmetry is indeed the field-theoretic definition and stochastic generalization of the concept of deterministic chaos. In addition, the previously proposed low-temperature classification of SDEs, i.e., thermodynamic equilibrium / noise-induced chaos ((anti)instanton condensation, intermittent) / ordinary chaos (non-integrability of the flow vector field), is complemented by the discussion of the high-temperature regime where the sharp boundary between the noise-induced and ordinary chaotic phases must smear out into a crossover, and at even higher temperatures the Q-symmetry is restored. The Weyl quantization is discussed in the context of the Ito-Stratonovich dilemma.
The Boltzmann equation from quantum field theory
NASA Astrophysics Data System (ADS)
Drewes, Marco; Mendizabal, Sebastián; Weniger, Christoph
2013-01-01
We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff-Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.
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
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean
F. J. Beron-Vera; M. J. Olascoaga; G. Haller; M. Farazmand; J. Trinanes; Y. Wang
2015-02-23
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 \\emph{Sargassum} distributions.
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.
Towards a quantum field theory of primitive string fields
Ruehl, W., E-mail: wue_ruehl@t-online.de [Technical University of Kaiserslautern, Department of Physics (Germany)
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.
A simple proof of orientability in colored group field theory
2012-01-01
Background Group field theory is an emerging field at the boundary between Quantum Gravity, Statistical Mechanics and Quantum Field Theory and provides a path integral for the gluing of n-simplices. Colored group field theory has been introduced in order to improve the renormalizability of the theory and associates colors to the faces of the simplices. The theory of crystallizations is instead a field at the boundary between graph theory and combinatorial topology and deals with n-simplices as colored graphs. Several techniques have been introduced in order to study the topology of the pseudo-manifold associated to the colored graph. Although of the similarity between colored group field theory and the theory of crystallizations, the connection between the two fields has never been made explicit. Findings In this short note we use results from the theory of crystallizations to prove that color in group field theories guarantees orientability of the piecewise linear pseudo-manifolds associated to each graph generated perturbatively. Conclusions Colored group field theories generate orientable pseudo-manifolds. The origin of orientability is the presence of two interaction vertices in the action of colored group field theories. In order to obtain the result, we made the connection between the theory of crystallizations and colored group field theory. PMID:23984224
Compressible Lagrangian hydrodynamics without Lagrangian cells
Clark, R.A.
1985-01-01
Traditional Lagrangian hydrodynamic codes for time dependent, compressible, multimaterial problems in two dimensions use the same general method. A Lagrangian mesh is defined, which moves with the fluid and this mesh defines a set of Lagrangian cells. The mass in each cell remains fixed and the motion of the mesh determines the volume and hence the density of each cell. These methods work well until the mesh becomes distorted due to shear or turbulence. Large distortions cause computer codes to quickly grind to a halt. The usual solution to distortion is to ''rezone'' the mesh. Here we move the mesh points artificially so as to reduce distortions and then map the quantities from the old mesh to the new. This results in unwanted diffusion of mass, momentum and energy throughout the mesh. Even with rezoning, few Lagrangian codes can handle more than limited distortions. Recently, what we call ''Free-Lagrangian'' codes have been developed specifically to handle large distortions. These codes, in addition to adjusting the mesh points, can reconnect mesh points, thus creating new cells. While Free-Lagrangian codes can handle virtually any distortion, they are even more diffusive than rezoners. We are trying a different aproach to the problem. We abandon the idea of Lagrangian cells entirely. In the next section we will discuss how the conservation equations can be solved directly without resorting to Lagrangian cells. Next we will give some examples of calculations using this method. Finally, we will give details of the calculational method presently being used.
Pauli-Villars regulatization of supergravity and field theory anomalies
Gaillard, M.K.
1995-06-01
A procedure for Pauli-Villars regularization of locally and globally supersymmetric theories is described. Implications for specific theories, especially those obtained from superstrings, are discussed with emphasis on the role of field theory anomalies.
Aspects of hot Galilean field theory
NASA Astrophysics Data System (ADS)
Jensen, Kristan
2015-04-01
We reconsider general aspects of Galilean-invariant thermal field theory. Using the proposal of our companion paper, we recast non-relativistic hydrodynamics in a manifestly covariant way and couple it to a background spacetime. We examine the concomitant consequences for the thermal partition functions of Galilean theories on a time-independent, but weakly curved background. We work out both the hydrodynamics and partition functions in detail for the example of parity-violating normal fluids in two dimensions to first order in the gradient expansion, finding results that differ from those previously reported in the literature. As for relativistic field theories, the equality-type constraints imposed by the existence of an entropy current appear to be in one-to-one correspondence with those arising from the existence of a hydrostatic partition function. Along the way, we obtain a number of useful results about non-relativistic hydrodynamics, including a manifestly boost-invariant presentation thereof, simplified Ward identities, the systematics of redefinitions of the fluid variables, and the positivity of entropy production.
Algebraic quantum field theory in curved spacetimes
Christopher J. Fewster; Rainer Verch
2015-04-02
This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a category of ($C^*$)-algebras obeying supplementary conditions. Among other things: (a) the key idea of relative Cauchy evolution is described in detail, and related to the stress-energy tensor; (b) a systematic "rigidity argument" is used to generalise results from flat to curved spacetimes; (c) a detailed discussion of the issue of selection of physical states is given, linking notions of stability at microscopic, mesoscopic and macroscopic scales; (d) the notion of subtheories and global gauge transformations are formalised; (e) it is shown that the general framework excludes the possibility of there being a single preferred state in each spacetime, if the choice of states is local and covariant. Many of the ideas are illustrated by the example of the free Klein-Gordon theory, which is given a new "universal definition".
Aspects of hot Galilean field theory
Kristan Jensen
2014-11-25
We reconsider general aspects of Galilean-invariant thermal field theory. Using the proposal of our companion paper, we recast non-relativistic hydrodynamics in a manifestly covariant way and couple it to a background spacetime. We examine the concomitant consequences for the thermal partition functions of Galilean theories on a time-independent, but weakly curved background. We work out both the hydrodynamics and partition functions in detail for the example of parity-violating normal fluids in two dimensions to first order in the gradient expansion, finding results that differ from those previously reported in the literature. As for relativistic field theories, the equality-type constraints imposed by the existence of an entropy current appear to be in one-to-one correspondence with those arising from the existence of a hydrostatic partition function. Along the way, we obtain a number of useful results about non-relativistic hydrodynamics, including a manifestly boost-invariant presentation thereof, simplified Ward identities, the systematics of redefinitions of the fluid variables, and the positivity of entropy production.
Hot Defect Superconformal Field Theory in an External Magnetic Field
Veselin G. Filev
2009-10-05
In this paper we investigate the influence of an external magnetic field on a flavoured holographic gauge theory dual to the D3/D5 intersection at finite temperature. Our study shows that the external magnetic field has a freezing effect on the confinement/ deconfinement phase transition. We construct the corresponding phase diagram. We investigate some thermodynamic quantities of the theory. A study of the entropy reveals enhanced relative jump of the entropy at the "chiral" phase transition. A study of the magnetization shows that both the confined and deconfined phases exhibit diamagnetic response. The diamagnetic response in the deconfined phase has a stronger temperature dependence reflecting the temperature dependence of the conductivity. We study the meson spectrum of the theory and analyze the stability of the different phases looking at both normal and quasi-normal semi-classical excitations. For the symmetry breaking phase we analyze the corresponding pseudo-Goldstone modes and prove that they satisfy non-relativistic dispersion relation.
On Superselection Theory of Quantum Fields in Low Dimensions
Michael Mueger
2009-09-14
We discuss finite local extensions of quantum field theories in low space time dimensions in connection with categorical structures and the question of modular invariants in conformal field theory, also touching upon purely mathematical ramifications.
Physics 221B: Solution to HW # 8 Quantum Field Theory
Murayama, Hitoshi
Physics 221B: Solution to HW # 8 Quantum Field Theory 1) Bosonic Grand-Partition Function The solution to this problem is outlined clearly in the beginning of the lecture notes `Quantum Field Theory II
Spectral density constraints in quantum field theory
NASA Astrophysics Data System (ADS)
Lowdon, Peter
2015-08-01
Determining the structure of spectral densities is important for understanding the behavior of any quantum field theory (QFT). However, the exact calculation of these quantities often requires a full nonperturbative description of the theory, which for physically realistic theories such as quantum chromodynamics (QCD) is currently unknown. Nevertheless, it is possible to infer indirect information about these quantities. In this paper we demonstrate an approach for constraining the form of spectral densities associated with QFT propagators, which involves matching the short distance expansion of the spectral representation with the operator product expansion (OPE) of the propagators. As an application of this procedure we analyze the scalar propagator in ?4 -theory and the quark propagator in QCD, and show that constraints are obtained on the spectral densities and the OPE condensates. In particular, it is demonstrated that the perturbative and nonperturbative contributions to the quark condensate in QCD can be decomposed, and that the nonperturbative contributions are related to the structure of the continuum component of the scalar spectral density.
The Dual Description of Long Distance QCD and the Effective Lagrangian for Constituent Quarks
Marshall Baker
1995-05-19
We describe long distance QCD by a dual theory in which the fundamental variables are dual potentials coupled to monopole fields and use this dual theory to determine the effective Lagrangian for constituent quarks. We find the color field distribution surrounding a quark anti-quark pair to first order in their velocities. Using these distributions we eliminate the dual potentials and obtain an effective interaction Lagrangian $L_I ( \\vec x_1 \\, , \\vec x_2 \\, ; \\vec v_1 \\, , \\vec v_2 )$ depending only upon the quark and anti-quark coordinates and velocities, valid to second order in their velocities. We propose $ L_I $ as the Lagrangian describing the long distance interaction of constituent quarks.
A general construction of conformal field theories from scalar anti-de Sitter quantum field theories
NASA Astrophysics Data System (ADS)
Bertola, Marco; Bros, Jacques; Moschella, Ugo; Schaeffer, Richard
2000-10-01
We provide a new general setting for scalar interacting fields on the covering of a ( d+1 )-dimensional AdS spacetime. The formalism is used at first to construct a one-parameter family of field theories, each living on a corresponding spacetime submanifold of AdS, which is a cylinder R× Sd-1 . We then introduce a limiting procedure which directly produces Lüscher-Mack CFT's on the covering of the AdS asymptotic cone. Our generalized AdS ? CFT construction is nonperturbative, and is illustrated by a complete treatment of two-point functions, the case of Klein-Gordon fields appearing as particularly simple in our context. We also show how the Minkowskian representation of these boundary CFT's can be directly generated by an alternative limiting procedure involving Minkowskian theories in horocyclic sections (nowadays called ( d- 1)-branes, 3-branes for AdS 5 ). These theories are restrictions to the brane of the ambient AdS field theory considered. This provides a more general correspondence between the AdS field theory and a Poincaré invariant QFT on the brane, satisfying all the Wightman axioms. The case of two-point functions is again studied in detail from this viewpoint as well as the CFT limit on the boundary.
Structure of Lanczos-Lovelock Lagrangians in critical dimensions
NASA Astrophysics Data System (ADS)
Yale, Alexandre; Padmanabhan, T.
2011-06-01
The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D-dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general covariance, and (c) have field equations involving derivatives of the metric tensor only up to second order. The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor. The field equations resulting from it become trivial in the critical dimension D = 2 m and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language. While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in D = 2 m. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In particular, we demonstrate that, in two dimensions, {R ?{-g} = partial_j R^j} for a doublet of functions R j = ( R 0, R 1) which depends only on the metric and its first derivatives. We explicitly construct families of such R j -s in two dimensions. We also address related questions regarding the Gauss-Bonnet Lagrangian in D = 4. Finally, we demonstrate the relation between the Chern-Simons form and the mth order Lanczos-Lovelock Lagrangian.
The effective field theory treatment of quantum gravity
Donoghue, John F. [Department of Physics, University of Massachusetts, Amherst, MA 01003 (United States)
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.
On open-closed extension of boundary string field theory
Akira Ishida; Shunsuke Teraguchi
2012-07-11
We investigate a classical open-closed string field theory whose open string sector is given by boundary string field theory. The open-closed interaction is introduced by the overlap of a boundary state with a closed string field. With the help of the Batalin-Vilkovisky formalism, the closed string sector is determined to be the HIKKO closed string field theory. We also discuss the gauge invariance of this theory in both open and closed string sides.
Infinite circumference limit of conformal field theory
NASA Astrophysics Data System (ADS)
Ishibashi, Nobuyuki; Tada, Tsukasa
2015-08-01
We argue that an infinite circumference limit can be obtained in two-dimensional conformal field theory by adopting {L}0-({L}1+{L}-1)/2 as a Hamiltonian instead of L0. The theory obtained has a circumference of infinite length and hence exhibits a continuous and heavily degenerated spectrum as well as the continuous Virasoro algebra. The choice of this Hamiltonian was inspired partly by the so-called sine-square deformation, which is found in the study of a certain class of quantum statistical systems. The enigmatic behavior of sine-square deformed systems such as the sharing of their vacuum states with the closed boundary systems can be understood by the appearance of an infinite circumference.
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.
Heterotic ?'-corrections in Double Field Theory
NASA Astrophysics Data System (ADS)
Bedoya, Oscar A.; Marqués, Diego; Núñez, Carmen
2014-12-01
We extend the generalized flux formulation of Double Field Theory to include all the first order bosonic contributions to the ?' expansion of the heterotic string low energy effective theory. The generalized tangent space and duality group are enhanced by ?' corrections, and the gauge symmetries are generated by the usual (gauged) generalized Lie derivative in the extended space. The generalized frame receives derivative corrections through the spin connection with torsion, which is incorporated as a new degree of freedom in the extended bein. We compute the generalized fluxes and find the Riemann curvature tensor with torsion as one of their components. All the four-derivative terms of the action, Bianchi identities and equations of motion are reproduced. Using this formalism, we obtain the first order ?' corrections to the heterotic Buscher rules. The relation of our results to alternative formulations in the literature is discussed and future research directions are outlined.
Lattice field theory simulations of graphene
Joaquín E. Drut; Timo A. Lähde
2009-04-21
We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene. We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods for the chiral condensate, which is the order parameter for the semimetal-insulator transition in graphene, induced by the Coulomb interaction between the massless electronic quasiparticles. The critical coupling and the associated exponents of this transition are determined by means of the logarithmic derivative of the chiral condensate and an equation-of-state analysis. A thorough discussion of finite-size effects is given, along with several tests of our calculational framework. These results strengthen the case for an insulating phase in suspended graphene, and indicate that the semimetal-insulator transition is likely to be of second order, though exhibiting neither classical critical exponents, nor the predicted phenomenon of Miransky scaling.
J. Bricmont; J. Fröhlich
1985-01-01
We analyze the particle structure of lattice field theories, in particular of lattice gauge theories with matter fields. We introduce and exploit the idea that particle structure in lattice field theory is intimately related to the statistical mechanics of fluctuating random paths and random tubes which arise in random walk and random surface representations of the lattice theories. Our methods
Point-form quantum field theory
NASA Astrophysics Data System (ADS)
Biernat, E. P.; Klink, W. H.; Schweiger, W.; Zelzer, S.
2008-06-01
We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form x?x? = ?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 Poincaré 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.
Transfer operators and topological field theory
Igor V. Ovchinnikov
2014-10-24
The transfer operator (TO) formalism of the dynamical systems (DS) theory is reformulated here in terms of the recently proposed cohomological theory (ChT) of stochastic differential equations (SDE). It turns out that the stochastically generalized TO (GTO) of the DS theory is the finite-time ChT Fokker-Planck evolution operator. As a result comes the supersymmetric trivialization of the so-called sharp trace and sharp determinant of the GTO, with the former being the Witten index of the ChT. Moreover, the Witten index is also the stochastic generalization of the Lefschetz index so that it equals the Euler characteristic of the (closed) phase space for any flow vector field, noise metric, and temperature. The enabled possibility to apply the spectral theorems of the DS theory to the ChT Fokker-Planck operators allows to extend the previous picture of the spontaneous topological supersymmetry (Q-symmetry) breaking onto the situations with negative ground state's attenuation rate. The later signifies the exponential growth of the number of periodic solutions/orbits in the large time limit, which is the unique feature of chaotic behavior proving that the spontaneous breakdown of Q-symmetry is indeed the field-theoretic definition and stochastic generalization of the concept of deterministic chaos. In addition, the previously proposed low-temperature classification of SDE's, i.e., thermodynamic equilibrium / noise-induced chaos ((anti-)instanton condensation) / ordinary chaos (non-integrability), is complemented by the discussion of the high-temperature regime where the sharp boundary between the noise-induced and ordinary chaotic phases must smear out into a crossover, and at even higher temperatures the Q-symmetry is restored. An unambiguous resolution of the Ito-Stratonovich dilemma in favor of the Stratonovich approach and/or Weyl quantization is also presented.
Locality in Free String Field Theory J. Dimock \\Lambda
Locality in Free String Field Theory J. Dimock \\Lambda Dept. of Mathematics SUNY at Buffalo Buffalo field theory is local. The question for interacting strings is completely unsettled, since the theory, NY 14214 April 27, 1998 Abstract Free string field operators are constructed for the open bosonic
Galois Groups in Rational Conformal Field Theory
Doron Gepner
2006-08-23
It was established before that fusion rings in a rational conformal field theory (RCFT) can be described as rings of polynomials, with integer coefficients, modulo some relations. We use the Galois group of these relations to obtain a local set of equation for the points of the fusion variety. These equations are sufficient to classify all the RCFT, Galois group by Galois group. It is shown that the Galois group is equivalent to the pseudo RCFT group. We prove that the Galois groups encountered in RCFT are all abelian, implying solvability by radicals of the modular matrix.
Compact boson stars in K field theories
NASA Astrophysics Data System (ADS)
Adam, C.; Grandi, N.; Klimas, P.; Sánchez-Guillén, J.; Wereszczy?ski, A.
2010-11-01
We study a scalar field theory with a non-standard kinetic term minimally coupled to gravity. We establish the existence of compact boson stars, that is, static solutions with compact support of the full system with self-gravitation taken into account. Concretely, there exist two types of solutions, namely compact balls on the one hand, and compact shells on the other hand. The compact balls have a naked singularity at the center. The inner boundary of the compact shells is singular, as well, but it is, at the same time, a Killing horizon. These singular, compact shells therefore resemble black holes.
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.
OPE Convergence in Conformal Field Theory
Duccio Pappadopulo; Slava Rychkov; Johnny Espin; Riccardo Rattazzi
2015-06-12
We clarify questions related to the convergence of the OPE and conformal block decomposition in unitary Conformal Field Theories (for any number of spacetime dimensions). In particular, we explain why these expansions are convergent in a finite region. We also show that the convergence is exponentially fast, in the sense that the operators of dimension above Delta contribute to correlation functions at most exp(-a Delta). Here the constant a>0 depends on the positions of operator insertions and we compute it explicitly.
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.
Quantum Field Theory in Accelerated Frames
Dasgupta, Arundhati
2015-01-01
In this paper we re-investigate the Bogoliubov transformations which relate the Minkowski inertial vacuum to the vacuum of an accelerated observer. We implement the transformation using a non-unitary operator used in formulations of irreversible systems by Prigogine. We derive a Lyapunov function which signifies an irreversible time flow. We extend the formalism to the black hole space-time which has similar near-horizon geometry of an accelerated observer, and in addition show that thermalization is due to presence of black hole and white hole regions. Finally we discuss an attempt to generalize quantum field theory for accelerated frames using this new connection to Prigogine transformations.
A Matrix model from string field theory
Zeze, Syoji
2015-01-01
We demonstrate that a Hermitian matrix model can be derived from level truncated open string field theory with Chan-Paton factors. The Hermitian matrix is coupled with a scalar and a $U(N)$ vector which are responsible for the D-brane at the tachyon vacuum. Effective potential for the scalar is evaluated both in finite and large $N$. Increase of potential height is observed in both examples. The large $N$ matrix integral is identified with a system of $N$ ZZ branes and a ghost FZZT brane.
The Heisenberg group and conformal field theory
Hessel Posthuma
2011-05-24
A mathematical construction of the conformal field theory (CFT) associated to a compact torus, also called the "nonlinear Sigma-model" or "lattice-CFT", is given. Underlying this approach to CFT is a unitary modular functor, the construction of which follows from a "Quantization commutes with reduction"- type of theorem for unitary quantizations of the moduli spaces of holomorphic torus-bundles and actions of loop groups. This theorem in turn is a consequence of general constructions in the category of affine symplectic manifolds and their associated generalized Heisenberg groups.
Quantum Field Theory on Curved Noncommutative Spacetimes
Schenkel, Alexander
2011-01-01
We summarize our recently proposed approach to quantum field theory on noncommutative curved spacetimes. We make use of the Drinfel'd twist deformed differential geometry of Julius Wess and his group in order to define an action functional for a real scalar field on a twist-deformed time-oriented, connected and globally hyperbolic Lorentzian manifold. The corresponding deformed wave operator admits unique deformed retarded and advanced Green's operators, provided we pose a support condition on the deformation. The solution space of the deformed wave equation is constructed explicitly and can be canonically equipped with a (weak) symplectic structure. The quantization of the solution space of the deformed wave equation is performed using *-algebras over the ring C[[\\lambda
Quantum Field Theory on Curved Noncommutative Spacetimes
Alexander Schenkel
2011-01-24
We summarize our recently proposed approach to quantum field theory on noncommutative curved spacetimes. We make use of the Drinfel'd twist deformed differential geometry of Julius Wess and his group in order to define an action functional for a real scalar field on a twist-deformed time-oriented, connected and globally hyperbolic Lorentzian manifold. The corresponding deformed wave operator admits unique deformed retarded and advanced Green's operators, provided we pose a support condition on the deformation. The solution space of the deformed wave equation is constructed explicitly and can be canonically equipped with a (weak) symplectic structure. The quantization of the solution space of the deformed wave equation is performed using *-algebras over the ring C[[\\lambda
Causality Is Inconsistent With Quantum Field Theory
Wolf, Fred Alan [Global Quantum Physics Educational Company, San Francisco CA (United States)
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.
Dori Bejleri; Matilde Marcolli
2012-09-21
In this paper we discuss some questions about geometry over the field with one element, motivated by the properties of algebraic varieties that arise in perturbative quantum field theory. We follow the approach to F1-geometry based on torified schemes. We first discuss some simple necessary conditions in terms of Euler characteristic and classes in the Grothendieck ring, then we give a blowup formula for torified varieties and we show that the wonderful compactifications of the graph configuration spaces, that arise in the computation of Feynman integrals in position space, admit an F1-structure. By a similar argument we show that the moduli spaces of curves of genus zero with n marked points admit an F1-structure. We also discuss conditions on hyperplane arrangements, a possible notion of embedded F1-structure and its relation to Chern classes, and questions on Chern classes of varieties with regular torifications.
Conformal field theory of critical Casimir forces
NASA Astrophysics Data System (ADS)
Emig, Thorsten; Bimonte, Giuseppe; Kardar, Mehran
2015-03-01
Thermal fluctuations of a critical system induce long-ranged Casimir forces between objects that couple to the underlying field. For two dimensional conformal field theories (CFT) we derive exact results for the Casimir interaction for a deformed strip and for two compact objects of arbitrary shape in terms of the free energy of a standard region (circular ring or flat strip) whose dimension is determined by the mutual capacitance of two conductors with the objects' shape; and a purely geometric energy that is proportional to conformal charge of the CFT, but otherwise super-universal in that it depends only on the shapes and is independent of boundary conditions and other details. The effect of inhomogenous boundary conditions is also discussed.
Classical and quantum theory of the massive spin-two field
Koenigstein, Adrian; Rischke, Dirk H
2015-01-01
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 Poincar\\'{e} 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 $J^{PC}=2^{-+}$ is, to our knowledge, given here for the first time.
Synchronous Lagrangian variational principles in General Relativity
NASA Astrophysics Data System (ADS)
Cremaschini, Claudio; Tessarotto, Massimo
2015-06-01
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in relativistic classical field theory which are either asynchronous or synchronous. The historical Einstein-Hilbert and Palatini variational formulations are found to belong to the first category. Nevertheless, it is shown that an alternative route exists which permits one to cast these principles in terms of equivalent synchronous Lagrangian variational formulations. The advantage is twofold. First, synchronous approaches allow one to overcome the lack of gauge symmetry of the asynchronous principles. Second, the property of manifest covariance of the theory is also restored at all levels, including the symbolic Euler-Lagrange equations, with the variational Lagrangian density being now identified with a 4-scalar. As an application, a joint synchronous variational principle holding both for the non-vacuum Einstein and Maxwell equations is displayed, with the matter source being described by means of a Vlasov kinetic treatment.
The universality question for noncommutative quantum field theory
Karl-Georg Schlesinger
2006-07-12
Present day physics rests on two main pillars: General relativity and quantum field theory. We discuss the deep and at the same time problematic interplay between these two theories. Based on an argument by Doplicher, Fredenhagen, and Roberts, we propose a possible universality property for noncommutative quantum field theory in the sense that any theory of quantum gravity should involve quantum field theories on noncommutative space-times as a special limit. We propose a mathematical framework to investigate such a universality property and start the discussion of its mathematical properties. The question of its connection to string theory could be a starting point for a new perspective on string theory.
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.
Strings and two-dimensional field theories
Naculich, S.G.
1988-01-01
In part I, the authors shows that the chiral zero modes of fermions coupled to an axionic string provide a physical realization of covariant gauge and gravitational anomalies in two dimensions. He develops a bosonized description of the chiral currents on the string, which allows us to treat the interactions of the zero modes with external fields. He uses this framework to calculate the scattering of electromagnetic waves off the string and to exhibit the quantization of charge of a closed axionic string bounding a domain wall. One-loop partition functions of rational conformal field theories are finite linear combinations of modular invariants associated with projective modular functions of a modular subgroup. In part II, he shows that, for normal subgroups with genus zero fundamental region, the functions which lead to physically acceptable partition functions are extremely limited in number, and can be found explicitly. He also shows that the conformal charge and weights of theories which factorize on these subgroups can only take on certain discrete values.
Four-dimensional deformed special relativity from group field theories
Girelli, Florian [SISSA, Via Beirut 2-4, 34014 Trieste, Italy and INFN, Sezione di Trieste (Italy); School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia); Livine, Etera R. [Laboratoire de Physique, ENS Lyon, CNRS UMR 5672, 46 Allee d'Italie, 69007 Lyon (France); Oriti, Daniele [Perimeter Institute for Theoretical Physics, 31 Caroline St, Waterloo, Ontario N2L 2Y5 (Canada); Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, Utrecht 3584 TD (Netherlands); Albert Einstein Institute, Am Muehlenberg 4, Golm (Germany)
2010-01-15
We derive a scalar field theory of the deformed special relativity type, living on noncommutative {kappa}-Minkowski space-time and with a {kappa}-deformed Poincare symmetry, from the SO(4,1) group field theory defining the transition amplitudes for topological BF theory in 4 space-time dimensions. This is done at a nonperturbative level of the spin foam formalism working directly with the group field theory (GFT). We show that matter fields emerge from the fundamental model as perturbations around a specific phase of the GFT, corresponding to a solution of the fundamental equations of motion, and that the noncommutative field theory governs their effective dynamics.
Refringence, field theory, and normal modes
C. Barcelo; S. Liberati; Matt Visser
2001-11-19
In a previous paper [gr-qc/0104001; Class. Quant. Grav. 18 (2001) 3595-3610] we have shown that the occurrence of curved spacetime ``effective Lorentzian geometries'' is a generic result of linearizing an arbitrary classical field theory around some non-trivial background configuration. This observation explains the ubiquitous nature of the ``analog models'' for general relativity that have recently been developed based on condensed matter physics. In the simple (single scalar field) situation analyzed in our previous paper, there is a single unique effective metric; more complicated situations can lead to bi-metric and multi-metric theories. In the present paper we will investigate the conditions required to keep the situation under control and compatible with experiment -- either by enforcing a unique effective metric (as would be required to be strictly compatible with the Einstein Equivalence Principle), or at the worst by arranging things so that there are multiple metrics that are all ``close'' to each other (in order to be compatible with the {\\Eotvos} experiment). The algebraically most general situation leads to a physical model whose mathematical description requires an extension of the usual notion of Finsler geometry to a Lorentzian-signature pseudo-Finsler geometry; while this is possibly of some interest in its own right, this particular case does not seem to be immediately relevant for either particle physics or gravitation. The key result is that wide classes of theories lend themselves to an effective metric description. This observation provides further evidence that the notion of ``analog gravity'' is rather generic.
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.
Noncommutative Tachyon from Background Independent Open String Field Theory
Kazumi Okuyama
2000-10-26
We analyze the tachyon field in the bosonic open string theory in a constant B-field background using the background independent open string field theory. We show that in the large noncommutativity limit the action of tachyon field is given exactly by the potential term which has the same form as in the case without B-field but the product of tachyon field is taken to be the star product.
Compressible Lagrangian hydrodynamics without Lagrangian cells
Clark, R.A.
1985-01-01
The formulation normally used to calculate compressible Lagrangian hydrodynamics in two dimensions is the following. First define a two-dimensional mesh containing a set of Lagrangian cells. Assign each cell a fixed mass. Compute the acceleration of the mesh points and move the points. The volume of the cell changes with the motion of the points. The changes in cell density, energy, and pressure are computed from the changes in volume. Difficulties occur when there are large distortions in the flow that cause similar large distortions in the Lagrangian cells. The usual solution is to somehow adjust the mesh as the calculation proceeds. This involves either moving individual mesh points or actually reconnecting the mesh. In either case, it becomes necessary to remap the mass from the old cells to the new. This necessarily produces some amount of undesirable numerical diffusion. When and how to adjust the mesh and how to accurately remap the mass and other variables so as to minimize numerical diffusion are the problems. One way to eliminate these problems is to abandon the idea of the Lagrangian cell since it is the distortion of the Lagrangian cell that is the cause of all the other problems. We discuss how the conservation equations can be solved directly without resorting to Lagrangian cells, and we give some examples of calculations using this method. Finally, we give details of the calculational method presently being used.