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1

Theory of Classical Higgs Fields. II. Lagrangians

We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $P\\to X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/H\\to X$ are treated as classical Higgs fields. In this theory, matter fields with an exact symmetry group $H$ are described by sections of a composite bundle $Y\\to P/H\\to X$. We show that their gauge $G$-invariant Lagrangian necessarily factorizes through a vertical covariant differential on $Y$ defined by a principal connection on an $H$-principal bundle $P\\to P/H$.

G. Sardanashvily; A. Kurov

2014-11-26

2

Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdS d space

We apply the BRST approach, developed for higher spin field theories, to Lagrangian construction for totally antisymmetric massive fermionic fields in AdSd space. As well as generic higher spin massive theories, the obtained Lagrangian theory is a reducible gauge model containing, besides the basic field, a number of auxiliary (Stückelberg) fields and the order of reducibility grows with the value

I. L. Buchbinder; V. A. Krykhtin; L. L. Ryskina

2009-01-01

3

Cosmic density and velocity fields in Lagrangian perturbation theory

A first- and second-order relation between cosmic density and peculiar-velocity fields is presented. The calculation is purely Lagrangian and it is derived using the second-order solutions of the Lagrange-Newton system obtained by Buchert & Ehlers. The procedure is applied to two particular solutions given generic initial conditions. In this approach, the continuity equation yields a relation between the over-density and peculiar-velocity fields that automatically satisfies Euler's equation because the orbits are derived from the Lagrange-Newton system. This scheme generalizes some results obtained by Nusser et al. (1991) in the context of the Zel'dovich approximation. As opposed to several other reconstruction schemes, in this approach it is not necessary to truncate the expansion of the Jacobian given by the continuity equation in order to calculate a first- or second-order expression for the density field. In these previous schemes, the density contrast given by (a) the continuity equation and (b) Euler's equation are mutually incompatible. This inconsistency arises as a consequence of an improper handling of Lagrangian and Eulerian coordinates in the analysis. Here, we take into account the fact that an exact calculation of the density is feasible in the Lagrangian picture and therefore an accurate and consistent description is obtained.

Mikel Susperregi; Thomas Buchert

1997-08-04

4

Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space

In this work we develop the BRST approach to Lagrangian construction for the massive integer higher spin fields in an arbitrary dimensional AdS space. The theory is formulated in terms of auxiliary Fock space. Closed nonlinear symmetry algebra of higher spin bosonic theory in AdS space is found and a method of deriving the BRST operator for such an algebra

I. L. Buchbinder; V. A. Krykhtin; P. M. Lavrov

2007-01-01

5

A study on relativistic lagrangian field theories with non-topological soliton solutions

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.

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

6

Partition Function in One, Two and Three Spatial Dimensions from Effective Lagrangian Field Theory

The systematic effective Lagrangian method was first formulated in the context of the strong interaction: chiral perturbation theory (CHPT) is the effective theory of Quantum Chromodynamics (QCD). It was then pointed out that the method can be transferred to the nonrelativistic domain -- in particular, to describe the low-energy properties of ferromagnets. Interestingly, whereas for Lorentz-invariant systems the effective Lagrangian method fails in one spatial dimension ($d_s$=1), it perfectly works for nonrelativistic systems in $d_s$=1. In the present brief review, we give an outline of the method and then focus on the partition function for ferromagnetic spin chains, ferromagnetic films and ferromagnetic crystals up to three loops in the perturbative expansion -- an accuracy never achieved by conventional condensed matter methods. We then compare ferromagnets in $d_s$=1,2,3 with the behavior of QCD at low temperatures by considering the pressure and the order parameter. The two apparently very different systems (ferromagnets and QCD) are related from a universal point of view based on the spontaneously broken symmetry. In either case, the low-energy dynamics is described by an effective theory containing Goldstone bosons as basic degrees of freedom.

Christoph P. Hofmann

2014-02-04

7

The Heisenberg-Euler Lagrangian as an example of an effective field theory

NASA Astrophysics Data System (ADS)

We review the beginning of the effective Lagrangian in QED that was first introduced in the literature by W. Heisenberg and H. Euler in 1936. Deviating from their way of calculating the one-loop effective correction to the classical Maxwell Lagrangian, we use Green's functions and adopt the Fock-Schwinger proper-time method. The important role of the Heisenberg-Euler effective Lagrangian is explicitly demonstrated for low-energy photon-photon processes.

Dittrich, Walter

2014-10-01

8

P- and T-Violating Lagrangians in Chiral Effective Field Theory and Nuclear Electric Dipole Moments

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.

Bsaisou, J; Nogga, A; Wirzba, A

2014-01-01

9

Lagrangian formalism for tensor fields

The Lagrangian formalism for tensor fields over differentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and metrics [$(\\bar{L}_n,g)$-spaces] is considered. The functional variation and the Lie variation of a Lagrangian density, depending on components of tensor fields (with finite rank) and their first and second covariant derivatives are established. A variation operator is determined and the corollaries of its commutation relations with the covariant and the Lie differential operators are found. The canonical (common) method of Lagrangians with partial derivatives (MLPD) and the method of Lagrangians with covariant derivatives (MLCD) are outlined. They differ from each other by the commutation relations the variation operator has to obey with the covariant and the Lie differential operator. The canonical and covariant Euler-Lagrange equations are found as well as their corresponding $(\\bar{L}_n,g)$-spaces. The energy-momentum tensors are considered on the basis of the Lie variation and the covariant Noether identities.

S. Manoff

2000-07-21

10

In this communication, we present a class of Brans-Dicke-like theories with a universal coupling between the scalar field and the matter Lagrangian. We show this class of theories naturally exhibits a decoupling mechanism between the scalar field and matter. As a consequence, this coupling leads to almost the same phenomenology as general relativity in the Solar System: the trajectories of massive bodies and the light propagation differ from general relativity only at the second post-Newtonian order. Deviations from general relativity are beyond present detection capabilities. However, this class of theories predicts a deviation of the gravitational redshift at a level detectable by the future ACES and STE/QUEST missions.

Olivier Minazzoli; Aurélien Hees

2013-08-13

11

Baryon chiral perturbation theory using a heavy fermion lagrangian

Baryon chiral perturbation theory is developed using an effective lagrangian in which the baryons appear as heavy static fields. The chiral logarithmic corrections to the axial current for semileptonic hyperon decay and for the analysis of the strangeness content of the proton are computed as examples. The corrections are as big as the lowest order values, which implies that F

Elizabeth Jenkins; Aneesh V. Manohar

1991-01-01

12

LE JOURNAL DE PHYSIQUE THE LAGRANGIAN THEORY OF POLYMER SOLUTIONS

LE JOURNAL DE PHYSIQUE THE LAGRANGIAN THEORY OF POLYMER SOLUTIONS AT INTERMEDIATE CONCENTRATIONS J'expĂŠrience. Abstract. 2014 De Gennes has shown that the properties of an isolated polymer in a solution (a chain in the absence of an external field. This result in generalized to the case of polymer solutions at intermediate

Boyer, Edmond

13

Using Lagrangian Perturbation Theory for Precision Cosmology

NASA Astrophysics Data System (ADS)

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-1 and z = 0.35 to better than 2%.

Sugiyama, Naonori S.

2014-06-01

14

String perturbation theory and effective Lagrangians

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.

Klebanov, I.

1987-09-01

15

Topics in low-dimensional field theory

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.

Crescimanno, M.J.

1991-04-30

16

Quaternionic quantum field theory

NASA Astrophysics Data System (ADS)

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 takes the form of either a functional integral with quaternion-imaginary Lagrangian, or a Schrödinger equation and transformation theory for quaternion-valued wave functions, with a quaternion-imaginary Hamiltonian. The connection between the two formulations is developed in detail, and many related issues, including the breakdown of the correspondence principle and the Hilbert space structure, are discussed.

Alder, Stephen L.

1986-12-01

17

Third-Order Lagrangian Perturbation Theory - Realization at High-Spatial Resolution

The Lagrangian theory of gravitational instability of homogeneous-isotropic Friedman-Lemaitre cosmogonies investigated and solved in the series of papers by Buchert (1989), (1992), Buchert & Ehlers (1993), Buchert (1993a,b), Ehlers & Buchert (1993), is illustrated. The third-order solution of this theory for generic initial conditions is presented and realized in a special case by employing methods of high-spatial resolution of the density field.

T. Buchert; A. G. Weiss

1993-10-13

18

Toy model for breaking super gauge theories at the effective Lagrangian level

We propose a toy model to illustrate how the effective Lagrangian for super QCD might go over to the one for ordinary QCD by a mechanism whereby the gluinos and squarks in the fundamental theory decouple below a given supersymmetry breaking scale m. The implementation of this approach involves a suitable choice of possible supersymmetry breaking terms. An amusing feature of the model is the emergence of the ordinary QCD degrees of freedom which were hidden in the auxiliary fields of the supersymmetric effective Lagrangian. {copyright} {ital 1997} {ital The American Physical Society}

Sannino, F.; Schechter, J. [Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States)] [Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States)

1998-01-01

19

Cosmological structure formation with augmented Lagrangian perturbation theory

NASA Astrophysics Data System (ADS)

We present a new fast and efficient approach to model structure formation with augmented Lagrangian perturbation theory (ALPT). Our method is based on splitting the displacement field into a long- and a short-range component. The long-range component is computed by second-order LPT (2LPT). This approximation contains a tidal non-local and non-linear term. Unfortunately, 2LPT fails on small scales due to severe shell crossing and a crude quadratic behaviour in the low-density regime. The spherical collapse (SC) approximation has been recently reported to correct for both effects by adding an ideal collapse truncation. However, this approach fails to reproduce the structures on large scales where it is significantly less correlated with the N-body result than 2LPT or linear LPT (the Zel'dovich approximation). We propose to combine both approximations using for the short-range displacement field the SC solution. A Gaussian filter with a smoothing radius rS is used to separate between both regimes. We use the result of 25 dark-matter-only N-body simulations to benchmark at z = 0 the different approximations: first-, second-, third-order LPT, SC and our novel combined ALPT model. This comparison demonstrates that our method improves previous approximations at all scales showing 25 and 75 per cent higher correlation than 2LPT with the N-body solution at k = 1 and 2 h Mpc-1, respectively. We conduct a parameter study to determine the optimal range of smoothing radii and find that the maximum correlation is achieved with rS = 4-5 h-1 Mpc. This structure formation approach could be used for various purposes, such as setting-up initial conditions for N-body simulations, generating mock galaxy catalogues, cosmic web analysis or for reconstructions of the primordial density fluctuations.

Kitaura, Francisco-Shu; Heß, Steffen

2013-08-01

20

Field Equations and Conservation Laws in the Nonsymmetric Gravitational Theory

The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived. Among these are the generalized Bianchi identities and the law of energy-momentum conservation. The Lagrangian density is expanded to second-order, and treated as an ``Einstein plus fields'' theory. From this, it is deduced that the energy is positive in the radiation zone.

J. Legare; J. W. Moffat

1994-12-02

21

The osp(1,2)-covariant Lagrangian quantization of irreducible massive gauge theories

NASA Astrophysics Data System (ADS)

The osp(1,2)-covariant Lagrangian quantization of general gauge theories is formulated which applies also to massive fields. The formalism generalizes the Sp(2)-covariant Batalin-Lavrov-Ty?tin (BLT) approach and guarantees symplectic invariance of the quantized action. The dependence of the generating functional of Green's functions on the choice of gauge in the massive case disappears in the limit m?0. Ward identities related to osp(1,2) symmetry are derived. Massive gauge theories with closed algebra are studied as an example.

Geyer, B.; Lavrov, P. M.; Mülsch, D.

1999-02-01

22

Augmented Lagrangian formulation of orbital-free density functional theory

NASA Astrophysics Data System (ADS)

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.

Suryanarayana, Phanish; Phanish, Deepa

2014-10-01

23

Infinite Class of PT -Symmetric Theories from One Timelike Liouville Lagrangian

NASA Astrophysics Data System (ADS)

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-i g ? exp (i a ? ) 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 m th energy level in the n th sector is given by Em ,n(m +1 /2 )2a2/(16 n2).

Bender, Carl M.; Hook, Daniel W.; Mavromatos, Nick E.; Sarkar, Sarben

2014-12-01

24

Infinite Class of PT-Symmetric Theories from One Timelike Liouville Lagrangian.

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

Bender, Carl M; Hook, Daniel W; Mavromatos, Nick E; Sarkar, Sarben

2014-12-01

25

Holography and defect conformal field theories

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

Oliver Dewolfe; Daniel Z. Freedman; Hirosi Ooguri

2002-01-01

26

We consider systems of higher spin gauge fields that are described by a free field Lagrangian and one interaction of arbitrary order $N$ that is local and satisfies abelian gauge invariance. Such "solitary" interactions are derived from Noether potentials solving the Noether equations. They are constructed using a free conformal field theory carried by the same flat space as the higher spin fields. In this field theory we consider $N$-loop functions of conserved, conformally covariant currents, they are UV divergent. The residue of the first order pole in the dimensional regularisation approach to the $N$-loop function is a local differential operator and is free of anomalies, so that current conservation and conformal covariance is maintained. Applying this operator to the higher spin fields, the Noether potential results. We study the cases $N=2, N=3$ and N=4. We argue that our N=3 vertex for any number of derivatives $\\Delta$ is identical with the known cubic interaction.

Werner Ruehl

2012-02-14

27

Lagrangian perturbation theory at one loop order: Successes, failures, and improvements

NASA Astrophysics Data System (ADS)

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.

Vlah, Zvonimir; Seljak, Uro; Baldauf, Tobias

2015-01-01

28

Adler-Kostant-Symes systems as Lagrangian gauge theories

It is well known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here a Lagrangian version of the reduction procedure is exhibited for those cases for which the underlying Lie algebra admits an invariant scalar product. This is achieved by constructing a Lagrangian with gauge symmetry in such a way that, by means of the Dirac algorithm, this Lagrangian reproduces the Adler-Kostant-Symes system whose Hamiltonian is the quadratic form associated with the scalar product on the Lie algebra.

L. Feher; A. Gabor

2002-02-22

29

Adler-Kostant-Symes systems as Lagrangian gauge theories

NASA Astrophysics Data System (ADS)

It is well-known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here a Lagrangian version of the reduction procedure is exhibited for those cases for which the underlying Lie algebra admits an invariant scalar product. This is achieved by constructing a Lagrangian with gauge symmetry in such a way that, by means of the Dirac algorithm, this Lagrangian reproduces the Adler-Kostant-Symes system whose Hamiltonian is the quadratic form associated with the scalar product on the Lie algebra.

Fehér, L.; Gábor, A.

2002-08-01

30

A Lagrangian theory of the classical spinning electron

NASA Technical Reports Server (NTRS)

A Lagrangian is defined that governs the dynamics of a classical electron with spin, moving under the influence of electromagnetic forces. The Euler-Lagrange equations associated with this Lagrangian for space-time position x exp-alpha provide a generalization of the Lorentz force law. The remaining Euler-Lagrange equations lead directly to the (generalized) Frenkel (1926)-Thomas (1927)-BMT (1959) equations.

Nash, P. L.

1984-01-01

31

About non standard Lagrangians in cosmology

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.

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

32

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.

Buchbinder, I L; Tsulaia, M

2015-01-01

33

Lagrangian formulation of higher spin theories on AdS space

In this short note we present a Lagrangian formulation for free bosonic Higher Spin fields which belong to massless reducible representations of D-dimensional anti de Sitter group using an ambient space formalism.

Angelos Fotopoulos; Kamal L. Panigrahi; Mirian Tsulaia

2006-01-01

34

Electromagnetic Field Theory BO THIDĂ? UPSILON BOOKS #12;#12;ELECTROMAGNETIC FIELD THEORY #12;#12;Electromagnetic Field Theory BO THIDĂ? Swedish Institute of Space Physics and Department of Astronomy and Space, Sweden UPSILON BOOKS Âˇ COMMUNA AB Âˇ UPPSALA Âˇ SWEDEN #12;Also available ELECTROMAGNETIC FIELD THEORY

Hart, Gus

35

Introduction Classical Field Theory

Introduction Classical Field Theory Locally Covariant Quantum Field Theory Renormalization Time evolution Conclusions and outlook Locality and Algebraic Structures in Field Theory Klaus Fredenhagen IIÂ¨utsch and Pedro Lauridsen Ribeiro) Klaus Fredenhagen Locality and Algebraic Structures in Field Theory #12

Baer, Christian

36

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.

Washington Taylor

2006-06-28

37

The Lagrangian formulation of strong-field quantum electrodynamics in a plasma

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.

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

38

The Lagrangian formulation of strong-field quantum electrodynamics in a plasma

NASA Astrophysics Data System (ADS)

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.

Raicher, Erez; Eliezer, Shalom; Zigler, Arie

2014-05-01

39

BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space

We develop a general gauge-invariant Lagrangian construction for half-integer higher spin fields in the AdS space of any dimension. Starting with a formulation in terms of an auxiliary Fock space, we obtain closed nonlinear symmetry algebras of higher spin fermionic fields in the AdS space and find the corresponding BRST operator. A universal procedure for constructing gauge-invariant Lagrangians describing the

I. L. Buchbinder; V. A. Krykhtin; A. A. Reshetnyak

2007-01-01

40

On background-independent open-string field theory

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

Edward Witten

1992-01-01

41

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasilinear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order in the series of papers by Buchert (1989, 1992, 1993a), Buchert \\& Ehlers (1993), Buchert (1993b), Ehlers \\& Buchert (1993), is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work (Coles \\etal 1993, Melott \\etal 1993, Melott 1993) 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'' (Zel'dovich 1970, 1973, 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 $\\sigma \\approx 2$). 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-index $n=-1$) using cross-correlation statistics employed in

T. Buchert; A. L. Melott; A. G. Weiss

1993-09-30

42

On exact tachyon potential in open string field theory

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

Anton A. Gerasimov; Samson L. Shatashvili

2000-01-01

43

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability--Theory

NASA Astrophysics Data System (ADS)

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.

Andreussi, T.; Morrison, P. J.; Pegoraro, F.

2013-09-01

44

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stabilityTheory

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.

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. [Universitŕ di Pisa, Dipartimento di Fisica E. Fermi, Pisa 56127 (Italy)] [Universitŕ di Pisa, Dipartimento di Fisica E. Fermi, Pisa 56127 (Italy)

2013-09-15

45

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

NASA Technical Reports Server (NTRS)

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.

Buchert, T.; Melott, A. L.; Weiss, A. G.

1993-01-01

46

NASA Astrophysics Data System (ADS)

String theory has emerged as the leading candidate for a unified field theory of all known forces. However, it is impossible to trust the various phenomenological predictions of superstring theory based on classical solutions alone. It appears that the crucial problem of the theory, breaking ten dimensional space-time down to four dimensions, must be solved nonperturbatively before we can extract reliable predictions. String field theory may be the only formalism in which we can resolve this decisive question. Only a rigorous calculation of the true vacuum of the theory will determine which of the many classical solutions the theory actually predicts. In this review article, we summarize the rapid progress in constructing string field theory actions, such as the development of the covariant BRST theory. We also present the newer geometric formulation of string field theory, from which the BRST theory and the older light cone theory can be derived from first principles. This geometric formulation allows us to derive the complete field theory of strings from two geometric principles, in the same way that general relativity and Yang-Mills theory can be derived from two principles based on global and local symmetry. The geometric formalism therefore reduces string field theory to a problem of finding an invariant under a new local gauge group we call the universal string group (USG). Thus, string field theory is the gauge theory of the universal string group in much the same way that Yang-Mills theory is the gauge theory of SU(N). Thus, the geometric formulation places superstring theory on the same rigorous group theoretical level as general relativity and gauge theory.

Kaku, Michio

47

Quantum Field Theory and Representation Theory

Quantum Field Theory and Representation Theory Peter Woit woit@math.columbia.edu Department of Mathematics Columbia University Quantum Field Theory and Representation Theory Â p.1 #12;Outline of the talk Âˇ Quantum Mechanics and Representation Theory: Some History Quantum Field Theory and Representation Theory

Woit, Peter

48

Optimizing Higher-order Lagrangian Perturbation Theory for Cold Dark Matter Models

We report on the performance of Lagrangian perturbation theory up to the second order for the standard cold dark matter (SCDM) and broken scale invariance (BSI) scenarios. We normalize both models to the COBE data, the BSI model serves as an example of models which fit the small-scale power of galaxy surveys. We optimize Lagrangian perturbation solutions by removing small-scale power from the initial data and compare the results with those of numerical simulations. We find an excellent performance of the optimized Lagrangian schemes down to scales around the correlation length or smaller, depending on the statistics used for the comparison. The optimization scheme can be expressed in a way which is independent of the type of fluctuation spectrum and of the size of the simulations.

A. G. Weiss; S. Gottloeber; T. Buchert

1995-12-15

49

Anyon in an external electromagnetic field: Hamiltonian and Lagrangian formulations

We propose a simple model for a free relativistic particle of fractional spin in 2+1 dimensions. Using the Hamiltonian formulation with the set of constraints, we introduce the electromagnetic interaction of a charged anyon and obtain the Lagrangian. The Casimir operator of the extended algebra, which is the first-class constraint, is obtained and gives the equation of motion of the anyon. In particular, from the latter it follows that the gyromagnetic ratio for a charged anyon is two due to the parallelness of spin and momentum of the particle in 2+1 dimensions. The canonical quantization is also considered.

Chaichian, M.; Felipe, R.G.; Martinez, D.L. (High Energy Physics Laboratory, Department of Physics, P.O. Box 9 (Siltavuorenpenger 20 C), SF-00014, University of Helsinki (Finland) Research Institute for High Energy Physics, P.O. Box 9 (Siltavuorenpenger 20 C), SF-00014, University of Helsinki (Finland) Research Institute for Theoretical Physics, P.O. Box 9 (Siltavuorenpenger 20 C), SF-00014, University of Helsinki (Finland))

1993-11-22

50

Transport induced by mean-eddy interaction: I. Theory, and relation to Lagrangian lobe dynamics

NASA Astrophysics Data System (ADS)

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.

Ide, Kayo; Wiggins, Stephen

2015-02-01

51

Tulczyjew Triples in Higher Derivative Field Theory

The geometrical structure known as Tulczyjew triple has been used with success in analytical mechanics and first order field theory to describe a wide range of physical systems including Lagrangian/Hamiltonian systems with constraints and/or sources, or with singular Lagrangian. Starting from the first principles of the variational calculus we derive Tulczyjew triples for classical field theories of arbitrary high order, i.e.~depending on arbitrary high derivatives of the fields. A first triple appears as the result of considering higher order theories as first order ones with configurations being constrained to be holonomic jets. A second triple is obtained after a reduction procedure aimed at getting rid of nonphysical degrees of freedom. This picture we present is fully covariant and complete: it contains both Lagrangian and Hamiltonian formalisms, in particular the Euler-Lagrange equations. Notice that, the required Geometry of jet bundles is affine (as opposed to the linear Geometry of the tangent bundle). Accordinlgy, the notions of affine duality and affine phase space play a distinguished role in our picture. In particular the Tulczyjew triples in this paper consist of morphisms of double affine-vector bundles which, moreover, preserve suitable presymplectic structures.

Katarzyna Grabowska; Luca Vitagliano

2014-06-25

52

Lagrangian and Hamiltonian formalism for discontinuous fluid and gravitational field

The barotropic ideal fluid with step and delta-function discontinuities coupled to Einstein's gravity is studied. The discontinuities represent star surfaces and thin shells; only non-intersecting discontinuity hypersurfaces are considered. No symmetry (like eg. 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 straifgtforward.

P. Hajicek; J. Kijowski

1997-07-09

53

Applications of effective Lagrangians

Effective Lagrangians were originally used only at the tree level as so-called phenomenological Lagrangians since they were in general non-renormalizable. Today they are treated as effective field theories valid below a characteristic energy scale. Quantum corrections can then be calculated in a consistent way as for any renormalizable theory. A few applications of the Euler-Heisenberg Lagrangian for interacting photons at low energies are presented together with recent developments in the use of QED for non-relativistic systems. Finally, the ingredients of an effective theory for the electroweak sector of the Standard Model are discussed in the case of a non-linear realization of the Higgs mechanism using the Stueckelberg formalism.

Ravndal, Finn [Institute of Physics, University of Oslo, N-0316 Oslo (Norway)

1997-06-15

54

The effective field theory of multifield inflation

NASA Astrophysics Data System (ADS)

We generalize the Effective Field Theory of Inflation to include additional light scalar degrees of freedom that are in their vacuum at the time the modes of interest are crossing the horizon. In order to make the scalars light in a natural way we consider the case where they are the Goldstone bosons of a global symmetry group or are partially protected by an approximate supersymmetry. We write the most general Lagrangian that couples the scalar mode associated to the breaking of time translation during inflation to the additional light scalar fields. This Lagrangian is constrained by diffeomorphism invariance and the additional symmetries that keep the new scalars light. This Lagrangian describes the fluctuations around the time of horizon crossing and it is supplemented with a general parameterization describing how the additional fluctuating fields can affect cosmological perturbations. We find that multifield inflation can reproduce the non-Gaussianities that can be generated in single field inflation but can also give rise to new kinds of non-Gaussianities. We find several new three-point function shapes. We show that in multifield inflation it is possible to naturally suppress the three-point function making the four-point function the leading source of detectable non-Gaussianities. We find that under certain circumstances, i.e. if specific shapes of non-Gaussianities are detected in the data, one could distinguish between single and multifield inflation and sometimes even among the various mechanisms that kept the additional fields light.

Senatore, Leonardo; Zaldarriaga, Matias

2012-04-01

55

Optimizing Higher-Order Lagrangian Perturbation Theory for Standard CDM and BSI models

We investigate the performance of Lagrangian perturbation theory up to the second order for two scenarios of cosmological large-scale structure formation, SCDM (standard cold dark matter) and BSI (broken scale invariance). The latter model we study as a representative of COBE-normalized CDM models which fit the small-scale power of galaxy surveys. In this context we optimize the performance of the Lagrangian perturbation schemes by smoothing the small-scale fluctuations in the initial data. The results of the so obtained Lagrangian mappings are computed for a set of COBE-normalized SCDM and BSI initial data of different sizes and at different times. We compare these results against those obtained with a numerical PM-code. We find an excellent performance of the optimized Lagrangian schemes down to scales close to the correlation length. This is explained by the counterintuitive fact that nonlinearities in the model can produce more small-scale power, if initially such power is removed. The optimization scheme can be expressed in a way which is independent of the type of fluctuation spectrum and of the size of the simulations.

Arno G. Weiss; Stefan Gottloeber; Thomas Buchert

1995-05-24

56

Attractive Lagrangians for noncanonical inflation

Treating inflation as an effective theory, we expect the effective Lagrangian to contain higher-dimensional kinetic operators suppressed by the scale of UV physics. When these operators are powers of the inflaton kinetic energy, the scalar field can support a period of noncanonical inflation which is smoothly connected to the usual slow-roll inflation. We show how to construct noncanonical inflationary solutions to the equations of motion for the first time, and demonstrate that noncanonical inflation is an attractor in phase space for all small- and large-field models. We identify some sufficient conditions on the functional form of the Lagrangian that lead to successful noncanonical inflation since not every Lagrangian with higher-dimensional kinetic operators can support noncanonical inflation. This extends the class of known viable Lagrangians and excludes many Lagrangians which do not work.

Franche, Paul; Underwood, Bret; Wissanji, Alisha [Department of Physics, McGill University, 3600 University Street, Montreal, Quebec, H3A 2T8 (Canada); Gwyn, Rhiannon [Department of Physics, King's College London, Strand, London WC2R 2LS (United Kingdom)

2010-06-15

57

The nonlinear perturbation theory of gravitational instability is extended to include effects of both biasing and redshift-space distortions, which are inevitable in predicting observable quantities in galaxy surveys. Weakly nonlinear effects in galaxy clustering on large scales recently attracted great interest, since the precise determination of scales of baryon acoustic oscillations is crucial to investigate the nature of dark energy by galaxy surveys. We find that a local Lagrangian bias and redshift-space distortions are naturally incorporated in our formalism of perturbation theory with a resummation technique via the Lagrangian picture. Our formalism is applicable to any biasing scheme which is local in Lagrangian space, including the halo bias as a special case. Weakly nonlinear effects on halo clustering in redshift space are analytically given. We assume only a fundamental idea of the halo model: haloes form according to the extended Press-Schechter theory, and the spatial distributions are locally biased in Lagrangian space. There is no need for assuming the spherical collapse model to follow the dynamical evolution, which is additionally assumed in standard halo prescriptions. One-loop corrections to the power spectrum and correlation function of haloes in redshift space are explicitly derived and presented. Instead of relying on expensive numerical simulations, our approach provides an analytic way of investigating the weakly nonlinear effects, simultaneously including the nonlinear biasing and nonlinear redshift-space distortions. Nonlinearity introduces a weak scale dependence in the halo bias. The scale dependence is a smooth function in Fourier space, and the bias does not critically change the feature of baryon acoustic oscillations in the power spectrum. The same feature in the correlation function is less affected by nonlinear effects of biasing.

Matsubara, Takahiko [Department of Physics, Nagoya University, Chikusa, Nagoya, 464-8602 (Japan)

2008-10-15

58

NASA Astrophysics Data System (ADS)

Over the past few decades, in concert with ground-breaking experimental advances, condensed matter theory has drawn increasingly from the language of low-energy quantum field theory. This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. It emphasizes the development of modern methods of classical and quantum field theory with applications oriented around condensed matter physics. Topics covered include second quantization, path and functional field integration, mean-field theory and collective phenomena, the renormalization group, and topology. Conceptual aspects and formal methodology are emphasized, but the discussion is rooted firmly in practical experimental application. As well as routine exercises, the text includes extended and challenging problems, with fully worked solutions, designed to provide a bridge between formal manipulations and research-oriented thinking. This book will complement graduate level courses on theoretical quantum condensed matter physics. Spans the field of modern condensed matter theory focusing on field theory techniques Written to facilitate learning, with numerous challenging exercises, with fully worked solutions, aimed at physicists starting graduate-level courses The theoretical methods are firmly set in concrete experimental applications

Altland, Alexander; Simons, Ben

2006-06-01

59

(Non-)decoupled supersymmetric field theories

NASA Astrophysics Data System (ADS)

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).

Di Pietro, Lorenzo; Dine, Michael; Komargodski, Zohar

2014-04-01

60

BRST-invariant Lagrangian of spontaneously broken gauge theories in a noncommutative geometry

NASA Astrophysics Data System (ADS)

The quantization of spontaneously broken gauge theories in a noncommutative geometry (NCG) has been sought for some time, because quantization is crucial for making the NCG approach a reliable and physically acceptable theory. Lee, Hwang, and Ne'eman recently succeeded in realizing the BRST quantization of gauge theories in a NCG in the matrix derivative approach proposed by Coquereaux and co-workers. The present author has proposed a characteristic formulation to reconstruct a gauge theory in a NCG on the discrete space M4×ZN. Since this formulation is a generalization of the differential geometry on the ordinary manifold to that on the discrete manifold, it is more familiar than other approaches. In this paper, we show that within our formulation we can obtain the BRST-invariant Lagrangian in the same way as Lee, Hwang, and Ne'eman and apply it to the SU(2)×U(1) gauge theory.

Okumura, Yoshitaka

1996-09-01

61

New N = 2 superconformal field theories from M\\/F-theory orbifolds

We consider M-theory on (T2 × R2)\\/Zn with M5-branes wrapped on R2 One can probe this background with M5-branes wrapped on T2. The theories on the probes provide many new examples of N = 2 field theories without Lagrangian description. All these theories have Coulomb branches, and we find the corresponding Seiberg-Witten curves. The exact solution is encoded in a

Sergei Gukov; Anton Kapustin

1999-01-01

62

On p-Adic Sector of Open Scalar Strings and Zeta Field Theory

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.

Dragovich, Branko [Institute of Physics, Pregrevica 118, Zemun, P.O. Box 57, 11001 Belgrade (Serbia)

2010-06-17

63

Free field theory at null infinity and white noise calculus: a BMS invariant dynamical system

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.

Claudio Dappiaggi

2006-07-25

64

In defence of naivete: The conceptual status of Lagrangian QFT

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the "naive" quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work.

David Wallace

2001-12-23

65

Information channel capacity in the field theory estimation

NASA Astrophysics Data System (ADS)

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.

S?adkowski, J.; Syska, J.

2012-12-01

66

Bosonic String and String Field Theory: a solution using the holomorphic representation

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.

C. G. Bollini; M. C. Rocca

2009-08-20

67

NASA Astrophysics Data System (ADS)

The responses to tidal and/or wind forces of Lagrangian trajectories and Eulerian residual velocity in the southwestern Yellow Sea are investigated using a high-resolution circulation model. The simulated tidal harmonic constants agree well with observations and existing studies. The numerical experiment reproduces the long-range southeastward Eulerian residual current over the sloping bottom around the Yangtze Bank also shown in previous studies. However, the modeled drifters deployed at the northeastern flank of the Yangtze Bank in the simulation move northeastward, crossing over this strong southeastward Eulerian residual current rather than following it. Additional sensitivity experiments reveal that the influence of the Eulerian tidal residual currents on Lagrangian trajectories is relatively weaker than that of the wind driven currents. This result is consistent with the northeastward movement of ARGOS surface drifters actually released in the southwestern Yellow Sea. Further experiments suggest that the quadratic nature of the bottom friction is the crucial factor, in the southwestern Yellow Sea, for the weaker influence of the Eulerian tidal residual currents on the Lagrangian trajectories. This study demonstrates that the Lagrangian trajectories do not follow the Eulerian residual velocity fields in the shallow coastal regions of the southwestern Yellow Sea.

Wang, Bin; Hirose, Naoki; Moon, Jae-Hong; Yuan, Dongliang

2013-05-01

68

Linear Stability of Elliptic Lagrangian Solutions of the Planar Three-Body Problem via Index Theory

NASA Astrophysics Data System (ADS)

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.

Hu, Xijun; Long, Yiming; Sun, Shanzhong

2014-09-01

69

Twenty-first Century Lattice Gauge Theory: Results from the QCD Lagrangian

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.

Kronfeld, Andreas S.; /Fermilab

2012-03-01

70

NASA Astrophysics Data System (ADS)

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.

2014-12-01

71

Algebraic orbifold conformal field theories

The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank

Feng Xu

2000-01-01

72

Inductive approach towards a phenomenologically more satisfactory unififed field theory

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.

Rayski, J.; Rayski J.M. Jnr.

1985-11-01

73

BRST-invariant Lagrangian of spontaneously broken gauge theories in a noncommutative geometry

The quantization of spontaneously broken gauge theories in a noncommutative geometry (NCG) has been sought for some time, because quantization is crucial for making the NCG approach a reliable and physically acceptable theory. Lee, Hwang, and Ne{close_quote}eman recently succeeded in realizing the BRST quantization of gauge theories in a NCG in the matrix derivative approach proposed by Coquereaux and co-workers. The present author has proposed a characteristic formulation to reconstruct a gauge theory in a NCG on the discrete space {ital M}{sub 4}{times}{ital Z}{sub {sub {ital N}}}. Since this formulation is a generalization of the differential geometry on the ordinary manifold to that on the discrete manifold, it is more familiar than other approaches. In this paper, we show that within our formulation we can obtain the BRST-invariant Lagrangian in the same way as Lee, Hwang, and Ne{close_quote}eman and apply it to the SU(2){times}U(1) gauge theory. {copyright} {ital 1996 The American Physical Society.}

Okumura, Y. [Department of Natural Science, Chubu University, Kasugai, 487 (Japan)] [Department of Natural Science, Chubu University, Kasugai, 487 (Japan)

1996-09-01

74

Vlasov-Poisson in 1D for initially cold systems: post-collapse Lagrangian perturbation theory

NASA Astrophysics Data System (ADS)

We study analytically the collapse of an initially smooth, cold, self-gravitating collisionless system in one dimension. The system is described as a central 'S' shape in phase-space surrounded by a nearly stationary halo acting locally like a harmonic background on the S. To resolve the dynamics of the S under its self-gravity and under the influence of the halo, we introduce a novel approach using post-collapse Lagrangian perturbation theory. This approach allows us to follow the evolution of the system between successive crossing times and to describe in an iterative way the interplay between the central S and the halo. Our theoretical predictions are checked against measurements in entropy conserving numerical simulations based on the waterbag method. While our post-collapse Lagrangian approach does not allow us to compute rigorously the long-term behaviour of the system, i.e. after many crossing times, it explains the close to power-law behaviour of the projected density observed in numerical simulations. Pushing the model at late time suggests that the system could build at some point a very small flat core, but this is very speculative. This analysis shows that understanding the dynamics of initially cold systems requires a fine-grained approach for a correct description of their very central part. The analyses performed here can certainly be extended to spherical symmetry.

Colombi, Stéphane

2015-01-01

75

Beyond mean field theory: statistical field theory for neural networks

NASA Astrophysics Data System (ADS)

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.

Buice, Michael A.; Chow, Carson C.

2013-03-01

76

Field theory questions for string theory answers

We discuss the field theory of 3-brane probes in F-theory compactifications in two configurations, generalizing the work of Sen and of Banks, Douglas and Seiberg. One configuration involves several parallel 3-brane probes in F-theory compactified on T4\\/Z2, while the other invloves a compactification of F-theory on T6\\/Z2 × Z2 (which includes intersecting D4 singularities). In both cases string theory provides

Ofer Aharony; Jacob Sonnenschein; Stefan Theisen; Shimon Yankielowicz

1997-01-01

77

Gravitational Interaction of Higher Spin Massive Fields and String Theory

We discuss the problem of consistent description of higher spin massive\\u000afields coupled to external gravity. As an example we consider massive field of\\u000aspin 2 in arbitrary gravitational field. Consistency requires the theory to\\u000ahave the same number of degrees of freedom as in flat spacetime and to describe\\u000acausal propagation. By careful analysis of lagrangian structure of the

I. L. Buchbinder; V. D. Pershin

2000-01-01

78

Strings and Unified Field Theory

It is argued that string theory predicts unified field theory rather than general relativity coupled to matter fields. In unified field theory all the objects are geometrical, for strings the Kalb-Ramond matter field is identical to the asymmetric part of the metric except that the fields contribute to different sides of the field equations. The dilaton is related to the object of non-metricity.

Mark D. Roberts

2006-07-18

79

Application of Chiral Resonance Lagrangian Theories to the Muon g-2

NASA Astrophysics Data System (ADS)

We think that phenomenological resonance Lagrangian models, constrained by global fits from low energy hadron reaction data, can help to improve muon g-2 predictions. The main issue are those contributions which cannot be calculated by perturbative means: the hadronic vacuum polarization (HVP) effects and the hadronic light--by--light (HLbL) scattering contribution. I review recent progress in the evaluation of the HVP contribution within the broken Hidden Local Symmetry (HLS) framework, worked out in collaboration with M. Benayoun, P. David and L. DelBuono. Our HLS driven estimate reads a_mu (LO had)=(688.60+\\-4.24) 10^{-10} and we find a_mu (theory)= (11 659 177.65 +/- 5.76) 10^{-10}.

Jegerlehner, F.

80

Application of chiral resonance Lagrangian theories to the muon g-2

We think that phenomenological resonance Lagrangian models, constrained by global fits from low energy hadron reaction data, can help to improve muon g-2 predictions. The main issue are those contributions which cannot be calculated by perturbative means: the hadronic vacuum polarization (HVP) effects and the hadronic light--by--light (HLbL) scattering contribution. I review recent progress in the evaluation of the HVP contribution within the broken Hidden Local Symmetry (HLS) framework, worked out in collaboration with M. Benayoun, P. David and L. DelBuono. Our HLS driven estimate reads a_mu (LO had)=(688.60+\\-4.24) 10^{-10} and we find a_mu (theory)= (11 659 177.65 +/- 5.76) 10^{-10}.

Fred Jegerlehner

2013-12-13

81

Application of chiral resonance Lagrangian theories to the muon g-2

We think that phenomenological resonance Lagrangian models, constrained by global fits from low energy hadron reaction data, can help to improve muon g-2 predictions. The main issue are those contributions which cannot be calculated by perturbative means: the hadronic vacuum polarization (HVP) effects and the hadronic light--by--light (HLbL) scattering contribution. I review recent progress in the evaluation of the HVP contribution within the broken Hidden Local Symmetry (HLS) framework, worked out in collaboration with M. Benayoun, P. David and L. DelBuono. Our HLS driven estimate reads a_mu (LO had)=(688.60+\\-4.24) 10^{-10} and we find a_mu (theory)= (11 659 177.65 +/- 5.76) 10^{-10}.

Jegerlehner, Fred

2013-01-01

82

Mimetic Theory for Cell-Centered Lagrangian Finite Volume Formulation on General Unstructured Grids

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.

Sambasivan, Shiv Kumar [Los Alamos National Laboratory; Shashkov, Mikhail J. [Los Alamos National Laboratory; Burton, Donald E. [Los Alamos National Laboratory; Christon, Mark A. [Los Alamos National Laboratory

2012-07-19

83

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann--Lema\\^\\i tre cosmogonies investigated and solved up to the third order in the series of papers by Buchert (1989, 1992, 1993), Buchert \\& Ehlers (1993), Buchert (1994), Ehlers \\& Buchert (1994), is compared with numerical simulations. In this paper we study the dynamics of hierarchical models as a second step. In the first step (Buchert, Melott and Wei{\\ss} 1994) we analyzed the performance of the Lagrangian schemes for pancake models, i.e., models which initially have a truncated power spectrum. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non--linear regime............We find that for spectra with negative power--index the second--order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low--order statistics like the power--spectrum. In cases with much small--scale power the gain from the higher--order schemes is small, but still measurable. However, in contrast to the results found for pancake models, where the higher--order schemes get worse than TZA at late non--linear stages and on small scales, we here find that the second--order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these

A. L. Melott; T. Buchert; A. G. Weiß

1994-04-08

84

Towards a double field theory on para-Hermitian manifolds

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.

Vaisman, Izu [Department of Mathematics, University of Haifa, Haifa (Israel)] [Department of Mathematics, University of Haifa, Haifa (Israel)

2013-12-15

85

Logarithmic conformal field theory

NASA Astrophysics Data System (ADS)

Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more complicated non-rational theories. Examples include critical percolation, supersymmetric string backgrounds, disordered electronic systems, sandpile models describing avalanche processes, and so on. In each case, the non-rationality and non-unitarity of the CFT suggested that a more general theoretical framework was needed. Driven by the desire to better understand these applications, the mid-1990s saw significant theoretical advances aiming to generalise the constructs of rational CFT to a more general class. In 1994, Nahm introduced an algorithm for computing the fusion product of representations which was significantly generalised two years later by Gaberdiel and Kausch who applied it to explicitly construct (chiral) representations upon which the energy operator acts non-diagonalisably. Their work made it clear that underlying the physically relevant correlation functions are classes of reducible but indecomposable representations that can be investigated mathematically to the benefit of applications. In another direction, Flohr had meanwhile initiated the study of modular properties of the characters of logarithmic CFTs, a topic which had already evoked much mathematical interest in the rational case. Since these seminal theoretical papers appeared, the field has undergone rapid development, both theoretically and with regard to applications. Logarithmic CFTs are now known to describe non-local observables in the scaling limit of critical lattice models, for example percolation and polymers, and are an integral part of our understanding of quantum strings propagating on supermanifolds. They are also believed to arise as duals of three-dimensional chiral gravity models, fill out hidden sectors in non-rational theories with non-compact target spaces, and describe certain transitions in various incarnations of the quantum Hall effect. Other physical applications range from two-dimensional turbulence and non-equilibrium systems to aspects of the AdS/CFT correspondence and describing supersymmetric sigma models beyond the topological sector. We refer the reader to the

Gainutdinov, Azat; Ridout, David; Runkel, Ingo

2013-12-01

86

number of codewords, and , the Shannon entropy of the quantizer output. The goal was to characterize2220 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 54, NO. 5, MAY 2008 Lagrangian Vector Quantization With Combined Entropy and Codebook Size Constraints Robert M. Gray, Fellow, IEEE, TamĂĄs Linder

Linder, TamĂĄs

87

Lagrangian perturbation theory: exact one-loop power spectrum in general dark energy models

NASA Astrophysics Data System (ADS)

Recently, we found that the correction for the Einstein-de Sitter (EdS) assumption on the one-loop matter power spectrum for general dark energy models using the standard perturbation theory is not negligible (Lee et al., arXiv:1407.7325, 2014). Thus, we investigate the same problem by obtaining the exact displacement vector and kernels up to the third order for the general dark energy models in the Lagrangian perturbation theory (LPT). Using these exact solutions, we investigate the present one-loop matter power spectrum in the CDM model with to obtain a % error correction compared to that obtained from the EdS assumption for the mode. If we consider the total matter power spectrum, the correction is only % for the same mode. It means that the EdS assumption is a good approximation for the CDM model in LPT theory. However, one can use this method for general models where the EdS assumption is improper.

Lee, Seokcheon

2014-11-01

88

NASA Astrophysics Data System (ADS)

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 {mathbf{?}^*} , {[dot{J}]} : first Piola-Kirchhoff stress tensor and material derivative of the Jacobian of deformation and {mathbf{?}^{[0]}} , {dot{mathbf{\\varepsilon}}_{[0]}} ; second Piola-Kirchhoff stress tensor and material derivative of Green's strain tensor are precisely equivalent as the conjugate pairs {mathbf{?}^*} , {[dot{J}]} and {mathbf{?}^{[0]}} , {dot{mathbf{\\varepsilon}}_{[0]}} are transformable from each other. In the present work, we use {mathbf{?}^{[0]}} , {dot{mathbf{\\varepsilon}}_{[0]}} as conjugate pair. Two possible choices of dependent variables in the constitutive theories: ?, ?, {mathbf{?}^{[0]}} , {mathbf{q}} and ?, ?, {mathbf{\\varepsilon}_{[0]}} , {mathbf{q}} (in which ? is entropy density and {mathbf{q}} is heat vector) are explored based on conservation and balance laws. It is shown that the choice of ?, ?, {mathbf{\\varepsilon}_{[0]}} , {mathbf{q}} 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 {mathbf{\\varepsilon}_{[0]}} and {dot{mathbf{\\varepsilon}}_{[0]}} (or {mathbf{\\varepsilon}_{[1]}} ) in the constitutive theories. We generalize and consider strain rates {mathbf{\\varepsilon}_{[i]}} ; 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, {mathbf{?}^{[0]}} , {mathbf{\\varepsilon}_{[i]}} ; i = 0, 1, , n-1, ? and {mathbf{g}} are considered as arguments of ?, ?, {mathbf{\\varepsilon}_{[n]}} and {mathbf{q}} . When {dot{?}} 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 {mathbf{\\varepsilon}_{[i]}} and {mathbf{q}} . The stress tensor {mathbf{?}^{[0]}} is decomposed into equilibrium stress {{}_e mathbf{?}^{[0]}} and deviatoric stress {{}_d mathbf{?}^{[0]}} . Upon substituting this in the entropy inequality, we finally arrive at the inequality that must be satisfied by {{}_e mathbf{?}^{[0]}} , {{}_d mathbf{?}^{[0]}} and {mathbf{q}} . Derivations of the constitutive theory for {{}_e mathbf{?}^{[0]}} follow directly from {{}_e mathbf{?}^{(0)}} , equilibrium Cauchy stress tensor, and the constitutive theory for {mathbf{\\varepsilon}_{[n]}} is derived using the theory of generators and invariants. Constitutive theories for the heat vector {mathbf{q}} of up to orders n that are consistent (in terms of the argument tensors) with the constitutive theories for {mathbf{\\varepsilon}_{[n]}} 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 {mathbf{\\varepsilon}_{[n]}} and {mathbf{q}} using the combined generators of the argument tensors about a known configuration {\\underline{?}} 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 h

Surana, K. S.; Reddy, J. N.; Nunez, D.

2014-06-01

89

NASA Astrophysics Data System (ADS)

This paper presents ordered rate constitutive theories of orders m and n, i.e., (m, n) for finite deformation of homogeneous, isotropic, compressible and incompressible thermoviscoelastic solids with memory in Lagrangian description using entropy inequality in Gibbs potential ? as an alternate approach of deriving constitutive theories using entropy inequality in terms of Helmholtz free energy density ?. Second Piola-Kirchhoff stress ? [0] and Green's strain tensor ? [0] are used as conjugate pair. We consider ?, heat vector q, entropy density ? and rates of upto orders m and n of ? [0] and ? [0], i.e., ? [i]; i = 0, 1, . . . , m and ? [j]; j = 0, 1, . . . , n. We choose ?, ? [n], q and ? as dependent variables in the constitutive theories with ? [j]; j = 0, 1, . . . , n - 1, ? [i]; i = 0, 1, . . . , m, temperature gradient g and temperature ? as their argument tensors. Rationale for this choice is explained in the paper. Entropy inequality, decomposition of ? [0] into equilibrium and deviatoric stresses, the conditions resulting from entropy inequality and the theory of generators and invariants are used in the derivations of ordered rate constitutive theories of orders m and n in stress and strain tensors. Constitutive theories for the heat vector q (of up to orders m and n - 1) that are consistent (in terms of the argument tensors) with the constitutive theories for ? [n] (of up to orders m and n) are also derived. Many simplified forms of the rate theories of orders (m, n) are presented. Material coefficients are derived by considering Taylor series expansions of the coefficients in the linear combinations representing ? [n] and q using the combined generators of the argument tensors about a known configuration {{\\underline{\\varOmega}}} in the combined invariants of the argument tensors and temperature. It is shown that the rate constitutive theories of order one (m = 1, n = 1) when further simplified result in constitutive theories that resemble currently used theories but are in fact different. The solid continua characterized by these theories have mechanisms of elasticity, dissipation and memory, i.e., relaxation behavior or rheology. Fourier heat conduction law is shown to be an over simplified case of the rate theory of order one (m = 1, n = 1) for q. The paper establishes when there is equivalence between the constitutive theories derived here using ? and those presented in reference Surana et al. (Acta Mech. doi: 10.1007/s00707-014-1173-6, 2014) that are derived using Helmholtz free energy density ?. The fundamental differences between the two constitutive theories in terms of physics and their explicit forms using ? and ? are difficult to distinguish from the ordered theories of orders (m, n) due to complexity of expressions. However, by choosing lower ordered theories, the difference between the two approaches can be clearly seen.

Surana, K. S.; Reddy, J. N.; Nunez, Daniel

2014-11-01

90

Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field

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.

Yuri N. Obukhov; Tomas Ramos; Guillermo F. Rubilar

2012-09-13

91

Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field.

We develop a relativistic variational model for a nematic liquid crystal interacting with an electromagnetic 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 nonrelativistic models. As an application of our general formalism, we discuss the so-called Abraham-Minkowski controversy on the momentum of light in a medium. PMID:23030929

Obukhov, Yuri N; Ramos, Tomás; Rubilar, Guillermo F

2012-09-01

92

Gravitational radiation in d>4 from effective field theory

NASA Astrophysics Data System (ADS)

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 Einsteins quadrupole formula for any number of flat spacetime dimensions.

Cardoso, Vitor; Dias, Óscar J. C.; Figueras, Pau

2008-11-01

93

Screening of scalar fields in Dirac-Born-Infeld theory

NASA Astrophysics Data System (ADS)

We study a new screening mechanism which is present in Dirac-Born-Infeld (DBI)-like theories. A scalar field with a DBI-like Lagrangian is minimally coupled to matter. In the vicinity of sufficiently dense sources, nonlinearities in the scalar dominate and result in an approximately constant acceleration on a test particle, thereby suppressing the scalar force relative to gravity. Unlike generic P(X) or chameleon theories, screening happens within the regime of validity of the effective field theory thanks to the DBI symmetry. We derive an exact form for the field profile around multiple sources and determine the constraints on the theory parameters from tests of gravity. Perturbations around the spherically-symmetric background propagate superluminally, but we argue for a chronology protection analogous to Galileons. This is the first example of a screening mechanism for which quantum corrections to the theory are under control and exact solutions to cosmological N-body problems can be found.

Burrage, Clare; Khoury, Justin

2014-07-01

94

Nonlinear quantum equations: Classical field theory

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.

Rego-Monteiro, M. A.; Nobre, F. D. [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)] [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)

2013-10-15

95

Modern Classical Electrodynamics and Electromagnetic Radiation - Vacuum Field Theory Aspects

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.

N. N. Bogolubov; A. K. Prykarpatsky

2013-02-16

96

Algebraic orbifold conformal field theories.

The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time. PMID:11106383

Xu, F

2000-12-19

97

Algebraic orbifold conformal field theories

The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time. PMID:11106383

Xu, Feng

2000-01-01

98

Invariants from classical field theory

We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.

Diaz, Rafael [Grupo de Fisica-Matematica, Universidad Experimental Politecnica de las Fuerzas Armadas, Caracas 1010 (Venezuela); Leal, Lorenzo [Centro de Fisica Teorica y Computacional, Universidad Central de Venezuela, Caracas 1041-A (Venezuela)

2008-06-15

99

The effect of spatial and temporal resolutions and random errors on identification of Lagrangian coherent structures (LCSs) from Eulerian velocity fields is evaluated using two canonical flows: a two-dimensional vortex pair and a vortex ring formed by transient ejection of a jet from a tube. The flow field for the vortex pair case was steady and obtained analytically while the transient vortex ring flow was simulated using computational fluid dynamics. To evaluate resolution and random error effects, the flow fields were degraded by locally smoothing the flow and sampling it on a sparser grid to reduce spatial resolution, adding Gaussian distributed random noise to provide random errors, and/or subsampling the time series of vector fields to reduce the temporal resolution (the latter applying only for the vortex ring case). The degradation methods were meant to emulate distortions and errors introduced in common flow measurement methods such as digital particle image velocimetry. Comparing the LCS corresponding to the vortex boundary (separatrix) obtained from the degraded velocity fields with the true separatrix (obtained analytically for the vortex pair case or from high resolution, noise-free velocity fields for the vortex ring case) showed that noise levels as low as 5%-10% of the vortex velocity can cause the separatrix to significantly deviate from its true location in a random fashion, but the "mean" location still remained close to the true location. Temporal and spatial resolution degradations were found to primarily affect transient portions of the flow with strong spatial gradients. Significant deviations in the location of the separatrix were observed even for spatial resolutions as high as 2% of the jet diameter for the vortex ring case. PMID:20370296

Olcay, Ali B; Pottebaum, Tait S; Krueger, Paul S

2010-03-01

100

A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not contemplated by this function. Within this scheme, quantum mechanics, classical field theory and a quantum theory for scalar fields are discussed. As a by-product of the probabilistic scheme for classical field theory, the equations of the De Donder-Weyl theory for multi-dimensional variational problems are recovered.

Matteo Villani

2009-02-25

101

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.

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

102

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.

Thomas Buchert

1993-09-30

103

NASA Astrophysics Data System (ADS)

In the ocean, geostrophic velocity fields inferred from sea surface height (SSH) are often used to assess mixing structures and other properties. If the ocean is assumed to be in geostrophic balance, then the velocity of the geostrophic currents can be calculated. Here we investigate the differences between geostrophic and non-geostrophic velocity fields and mixing using a Regional Ocean Modeling System (ROMS) model of an idealized Eastern boundary current. A geostrophic velocity field was calculated from the model sea surface height and compared with model output surface velocities using both Eulerian and Lagrangian methods. Simulated test particles in MATLAB were placed globally and near the coast in each vector field and their trajectories were calculated by using the Runge Kutta 4th order method. By binning the particles and looking at their densities, we were able to measure where the particles accumulate and relate this to the difference in the two velocity fields. To calculate the different ways the particles accumulated in both vector fields the mixing efficiency and index of aggregation were used. Areas where the divergence of the ROMS vector field was non-zero were looked at in comparison to the difference in the magnitudes of the two velocities. I hypothesized that the areas of high velocities correlated with the high SSH gradient and sea surface temperature gradient. When the magnitude of the Rossby number for the ROMS vector field is less than one it should correlate to smaller differences between the two vector fields. Another hypothesis was that when the magnitude of the sea surface temperature (SST) or SSH gradient was high, there would be lots of error. Eddies and other ocean phenomena were looked at to see how well the geostrophic velocities modeled them. Where particles accumulate should correlate to areas of high biological accumulation, especially in the case of coastally released particles. This leads to higher rates of foraging by predators. It is important to understand the difference in the two velocity fields because we might be underestimating the biological processes using geostrophic velocity fields.

Prakash, A.; Harrison, C. S.

2011-12-01

104

Double field theory at order ?'

NASA Astrophysics Data System (ADS)

We investigate ?' corrections of bosonic strings in the framework of double field theory. The previously introduced "doubled ?'-geometry" gives ?'-deformed gauge transformations arising in the Green-Schwarz anomaly cancellation mechanism but does not apply to bosonic strings. These require a different deformation of the duality-covariantized Courant bracket which governs the gauge structure. This is revealed by examining the ?' corrections in the gauge algebra of closed string field theory. We construct a four-derivative cubic double field theory action invariant under the deformed gauge transformations, giving a first glimpse of the gauge principle underlying bosonic string ?' corrections. The usual metric and b-field are related to the duality covariant fields by non-covariant field redefinitions.

Hohm, Olaf; Zwiebach, Barton

2014-11-01

105

Hamilton-Jacobi equations and Brane associated Lagrangians

This article seeks to relate a recent proposal for the association of a covariant Field Theory with a string or brane Lagrangian to the Hamilton-Jacobi formalism for strings and branes. It turns out that since in this special case, the Hamiltonian depends only upon the momenta of the Jacobi fields and not the fields themselves, it is the same as a Lagrangian, subject to a constancy constraint. We find that the associated Lagrangians for strings or branes have a covariant description in terms of the square root of the same Lagrangian. If the Hamilton-Jacobi function is zero, rather than a constant, then it is in in one dimension lower, reminiscent of the `holographic' idea. In the second part of the paper, we discuss properties of these Lagrangians, which lead to what we have called `Universal Field Equations', characteristic of covariant equations of motion.

L. M. Baker; D. B. Fairlie

2000-11-15

106

Theory of fossil magnetic field

NASA Astrophysics Data System (ADS)

Theory of fossil magnetic field is based on the observations, analytical estimations and numerical simulations of magnetic flux evolution during star formation in the magnetized cores of molecular clouds. Basic goals, main features of the theory and manifestations of MHD effects in young stellar objects are discussed.

Dudorov, Alexander E.; Khaibrakhmanov, Sergey A.

2015-02-01

107

Einstein-aether theory with a Maxwell field: General formalism

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.

Alexander B. Balakin; José P. S. Lemos

2014-07-22

108

Einstein-aether theory with a Maxwell field: General formalism

NASA Astrophysics Data System (ADS)

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.

Balakin, Alexander B.; Lemos, José P. S.

2014-11-01

109

The $\\hbar$ Expansion in Quantum Field Theory

We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.

Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Hoyer, Paul; /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.

2010-10-27

110

Double field theory inspired cosmology

NASA Astrophysics Data System (ADS)

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.

Wu, Houwen; Yang, Haitang

2014-07-01

111

In this paper we present an efficient numerical scheme for the recently introduced Geodesic Active Fields (GAF) framework for geometric image registration. This framework considers the registration task as a weighted minimal surface problem. Hence, the data-term and the regularization-term are combined through multiplication in a single, parametrization invariant and geometric cost functional. The multiplicative coupling provides an intrinsic, spatially varying and data-dependent tuning of the regularization strength, while the parametrization invariance allows working with images of non-flat geometry, generally defined on any smoothly parametrizable manifold. The resulting energy-minimizing flow, however, has poor numerical properties. Here, we provide an efficient numerical scheme that uses a splitting approach: data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented Lagrangian approach. Our approach is more flexible than standard Gaussian regularization, since one can interpolate freely between isotropic Gaussian and anisotropic TV-like smoothing. In this work, we compare the Geodesic Active Fields method against the popular Demons method and three more recent state-of-the-art algorithms: NL-optical flow [1], MRF image registration [2], and landmark-enhanced large displacement optical flow [3]. Overall, we can show the advantages of the proposed FastGAF method. It compares strictly favorably against Demons, both in terms of registration speed and quality. Over the range of example applications, it also consistently produces results not far from more dedicated state-of-the-art methods, illustrating the flexibility of the proposed framework. PMID:23529085

Zosso, D; Bresson, X; Thiran, J

2013-03-20

112

Analytic progress in open string field theory

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 ...

Kiermaier, Michael Stefan

2009-01-01

113

Tachyonic Field Theory and Neutrino Mass Running

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.

U. D. Jentschura

2012-05-01

114

NASA Astrophysics Data System (ADS)

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 itthis 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 webfilaments, sheets and voids.

Sheth, Ravi K.; Chan, Kwan Chuen; Scoccimarro, Román

2013-04-01

115

The method of Lagrangians with covariant derivative (MLCD) is applied to a special type of Lagrangian density depending on scalar and vector fields as well as on their first covariant derivatives. The corresponding Euler-Lagrange's equations and energy-momentum tensors are found on the basis of the covariant Noether's identities.

Sawa Manoff

2002-05-07

116

Are Lagrangian stochastic models at odds with statistical theories of relative dispersion?

In an article on statistical modelling of turbulent relative dispersion, Franzese & Cassiani (2007, p. 402) commented on Lagrangian stochastic models and reported some concern about the consistency between statisti- cal and stochastic modelling of turbulent dispersion. In this short article, comparison of the two approaches is performed. As far as the dependence of models from turbulence constants is concerned, the two theoretical ap- proaches are found to be in perfect agreement eliminating every possible concern.

Maurizi, Alberto

2013-01-01

117

Yang-Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs effect

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

E. Cremmer; Sergio Ferrara; L. Girardello; A. van Proeyen

1983-01-01

118

Magnetic Yang-Mills Theory as an Effective Field Theory of the Gluon Plasma

We propose magnetic SU(N) pure gauge theory as an effective field theory describing the long distance nonperturbative magnetic response of the deconfined phase of Yang-Mills theory. The magnetic non-Abelian Lagrangian, unlike that of electrodynamics where there is exact electromagnetic duality, is not known explicitly, but here we regard the magnetic SU(N) Yang-Mills Lagrangian as the leading term in the long distance effective gauge theory of the plasma phase. In this treatment, which is applicable for a range of temperatures in the interval T_c magnetic energy profile around a spatial Wilson loop in the deconfined phase parallels the formation of an electric flux tube in the confined phase. We use the effective theory to calculate spatial Wilson loops and the magnetic charge density induced in the plasma by the corresponding color electric current loops. These calculations suggest that the deconfined phase of Yang-Mills theory has the properties of a closely-packed fluid of magnetically charged composite objects.

M. Baker

2009-01-20

119

The effective field theory of inflation/dark energy and the Horndeski theory

The effective field theory (EFT) of cosmological perturbations is a useful framework to deal with the low-energy degrees of freedom present for inflation and dark energy. We review the EFT for modified gravitational theories by starting from the most general action in unitary gauge that involves the lapse function and the three-dimensional geometric scalar quantities appearing in the Arnowitt-Deser-Misner (ADM) formalism. Expanding the action up to quadratic order in the perturbations and imposing conditions for the elimination of spatial derivatives higher than second order, we obtain the Lagrangian of curvature perturbations and gravitational waves with a single scalar degree of freedom. The resulting second-order Lagrangian is exploited for computing the scalar and tensor power spectra generated during inflation. We also show that the most general scalar-tensor theory with second-order equations of motion-Horndeski theory-belongs to the action of our general EFT framework and that the background equations of motion in Horndeski theory can be conveniently expressed in terms of three EFT parameters. Finally we study the equations of matter density perturbations and the effective gravitational coupling for dark energy models based on Horndeski theory, to confront the models with the observations of large-scale structures and weak lensing.

Shinji Tsujikawa

2014-09-01

120

Tail terms in gravitational radiation reaction via effective field theory

NASA Astrophysics Data System (ADS)

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 reproduce 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.

Foffa, Stefano; Sturani, Riccardo

2013-02-01

121

A Review of Noncommutative Field Theories

We present a brief review of selected topics in noncommutative field theories ranging from its revival in string theory, its influence on quantum field theories, its possible experimental signatures and ending with some applications in gravity and emergent gravity.

Victor O. Rivelles

2011-01-27

122

Introduction to string theory and conformal field theory

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.

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

123

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.

C. G. Bollini; A. L. De Paoli; M. C. Rocca

2008-11-17

124

Entropy Viscosity Method for Lagrangian Hydrodynamics and Central Schemes for Mean Field Games

Taylor-Green Vortex . . . . . . . . . . . . . . . . . . . . . 75 3.4.2 1D Sod Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.4.3 2D Sedov Explosion . . . . . . . . . . . . . . . . . . . . . . . . 81 3.4.4 2D Noh Implosion... Model . . . . . . . . . . . . . . . . . . . . . . . . 98 4. ALE HYDRODYNAMICS IN BLAST . . . . . . . . . . . . . . . . . . . . 104 4.1 Overview of the Lagrangian Phase in BLAST . . . . . . . . . . . . . 105 4.1.1 Viscous Regularization...

Tomov, Vladimir

2014-04-18

125

Quantum Field Theory in Graphene

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.

I. V. Fialkovsky; D. V. Vassilevich

2011-11-13

126

On Lagrangian formulations for mixed-symmetry HS fields on AdS spaces within BFV-BRST approach

The key aspects of a gauge-invariant Lagrangian description of massive and massless half-integer higher-spin fields in AdS spaces with a two-row Young tableaux $Y(s_1,s_2)$ are presented in an unconstrained description, as well as in off-shell formulations with algebraic constraints, on the basis of BFV-BRST operators for non-linear operator superalgebras, encoding the initial conditions realized by constraints in a Fock space and extracting the higher-spin fields from unitary representations of the AdS group.

A. A. Reshetnyak

2008-09-28

127

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

NASA Technical Reports Server (NTRS)

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.

Vandommelen, Leon L.; Cowley, Stephen J.

1989-01-01

128

(Super)gravity and Yang-Mills Theories as Generalized Topological Fields with Constraints

We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF formulations of general relativity and Yang-Mills theories, but also the N=1,2 chiral supergravities can be reformulated as these constrained generalized topological field theories once the free parameters in the Lagrangian are specially chosen. We also show that the Chern-Simons action on the boundary may naturally be induced from the generalized topological action in the bulk, rather than introduced by hand.

Yi Ling; Roh-Suan Tung; Han-Ying Guo

2003-10-15

129

Strongly coupled quantum field theory

I analyze numerically a two-dimensional {lambda}{phi}{sup 4} theory showing that in the limit of a strong coupling {lambda}{yields}{infinity} just the homogeneous solutions for time evolution are relevant in agreement with the duality principle in perturbation theory as presented in [M. Frasca, Phys. Rev. A 58, 3439 (1998)], being negligible the contribution of the spatial varying parts of the dynamical equations. A consequence is that the Green function method works for this nonlinear problem in the large coupling limit as in a linear theory. A numerical proof is given for this. With these results at hand, I built a strongly coupled quantum field theory for a {lambda}{phi}{sup 4} interacting field computing the first order correction to the generating functional. Mass spectrum of the theory is obtained turning out to be that of a harmonic oscillator with no dependence on the dimensionality of space-time. The agreement with the Lehmann-Kaellen representation of the perturbation series is then shown at the first order.

Frasca, Marco

2006-01-15

130

Large N limit of orbifold field theories

We consider a certain orbifoldization of the N = 4 field theories that leads to N = 2, 1, 0 field theories in four dimensions. These theories were recently analyzed using the string theory perturbation technique. It was found that in the large N limit all correlation functions of the orbifold theories coincide with those of N = 4, modulo

Michael Bershadsky; Andrei Johansen

1998-01-01

131

Bias in the Effective Field Theory of Large Scale Structures

We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local in space, but non-local in time, and we explain the observational consequences of this fact. We give an argument for why to a certain degree of accuracy the theory can be considered as quasi time-local and explain what the operator structure is in this case. We describe renormalization of the bias coefficients so that, after this and after upgrading the Eulerian calculation to a Lagrangian one, the perturbative series for galaxies correlation functions results in a manifestly convergent expansion in powers of $k/k_{\\rm NL}$ and $k/k_{\\rm M}$, where $k$ is the wavenumber of interest, $k_{\\rm NL}$ is the wavenumber associated to the non-linear scale, and $k_{\\rm M}$ is the comoving wavenumber enclosing the mass of a galaxy.

Leonardo Senatore

2014-11-05

132

A multisymplectic approach to defects in integrable classical field theory

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.

V. Caudrelier; A. Kundu

2015-01-26

133

Variational methods for field theories

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.

Ben-Menahem, S.

1986-09-01

134

Relativistic Quantum Mechanics and Field Theory

An accessible, comprehensive reference to modern quantum mechanics and field theory. In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis

Franz Gross

1999-01-01

135

N=1 field theories and fluxes in IIB string theory

Deformation of N=2 quiver gauge theories by adjoint masses leads to fixed manifolds of N=1 superconformal field theories. We elaborate on the role of the complex three-form flux in the IIB duals to these fixed point theories, primarily using field theory techniques. We study the moduli space at a fixed point and find that it is either the two (complex)

Richard Corrado; Nick Halmagyi

2005-01-01

136

Master equations for extended Lagrangian BRST symmetries

NASA Astrophysics Data System (ADS)

Starting from the requirement that a Lagrangian field theory be invariant under both Schwinger-Dyson BRST and Schwinger-Dyson anti-BRST symmetry, we derive the BRST-anti-BRST analogue of the Batalin-Vilkovisky formalism. This is done through standard Lagrangian gauge fixing respecting the extended BRST symmetry. The solutions of the resulting Master Equation and the gauge-fixing procedure for the quantum action can be brought into forms that coincide with those obtained earlier on algebraic grounds by Batalin, Lavrov and Tyutin.

H. Damgaard, Poul; De Jonghe, Frank

1993-05-01

137

N=1 field theory duality from M theory

We investigate Seiberg's N=1 field theory duality for four-dimensional supersymmetric QCD with the M-theory 5-brane. We find that the M-theory configuration for the magnetic dual theory arises via a smooth deformation of the M-theory configuration for the electric theory. The creation of Dirichlet 4-branes as Neveu-Schwarz 5-branes are passed through each other in type IIA string theory is given an

Martin Schmaltz; Raman Sundrum

1998-01-01

138

Haag's theorem in noncommutative quantum field theory

Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.

Antipin, K. V. [Moscow State University, Faculty of Physics (Russian Federation)] [Moscow State University, Faculty of Physics (Russian Federation); Mnatsakanova, M. N., E-mail: mnatsak@theory.sinp.msu.ru [Moscow State University, Skobeltsyn Institute of Nuclear Physics (Russian Federation); Vernov, Yu. S. [Russian Academy of Sciences, Institute for Nuclear Research (Russian Federation)] [Russian Academy of Sciences, Institute for Nuclear Research (Russian Federation)

2013-08-15

139

Effective field theory in nuclear physics

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.

Martin J. Savage

2000-12-12

140

COMPUTATIONAL CLASS FIELD THEORY H. Cohen

COMPUTATIONAL CLASS FIELD THEORY H. Cohen Number The* *ory, including the notions of discriminant, integral basis, Galois group, class grou* *p more is contained in my book [Coh0]. On class field theory itself, the subject matter of these notes

Cohen, Henri

141

Effective Field Theory in Nuclear Physics

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.

Martin J. Savage

2000-07-11

142

Motion of small bodies in classical field theory

NASA Astrophysics Data System (ADS)

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 bodys 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.

Gralla, Samuel E.

2010-04-01

143

A Lagrangian particle model has been adapted to examine human exposures to particulate matter < or = 10 microm (PM10) in agricultural settings. This paper reports the performance of the model in comparison to extensive measurements by elastic LIDAR (light detection and ranging). For the first time, the LIDAR measurements allowed spatially distributed and time dynamic measurements to be used to test the predictions of a field-scale model. The model outputs, which are three-dimensional concentration distribution maps from an agricultural disking operation, were compared with the LIDAR-scanned images. The peak cross-correlation coefficient and the offset distance of the measured and simulated plumes were used to quantify both the intensity and location accuracy. The appropriate time averaging and changes in accuracy with height of the plume were examined. Inputs of friction velocity, Monin-Obukhov length, and wind direction (1 sec) were measured with a three-axis sonic anemometer at a single point in the field (at 1.5-m height). The Lagrangian model of Wang et al. predicted the near-field concentrations of dust plumes emitted from a field disking operation with an overall accuracy of approximately 0.67 at 3-m height. Its average offset distance when compared with LIDAR measurements was approximately 38 m, which was 6% of the average plume moving distance during the simulation periods. The model is driven by weather measurements, and its near-field accuracy is highest when input time averages approach the turbulent flow time scale (3-70 sec). The model accuracy decreases with height because of smoothing and errors in the input wind field, which is modeled rather than measured at heights greater than the measurement anemometer. The wind steadiness parameter (S) can be used to quantify the combined effects of wind speed and direction on model accuracy. PMID:19947118

Wang, Junming; Hiscox, April L; Miller, David R; Meyer, Thomas H; Sammis, Ted W

2009-11-01

144

Lagrangian perfect fluids and black hole mechanics

The first law of black hole mechanics (in the form derived by Wald), is expressed in terms of integrals over surfaces, at the horizon and spatial infinity, of a stationary, axisymmetric black hole, in a diffeomorphism invariant Lagrangian theory of gravity. The original statement of the first law given by Bardeen, Carter and Hawking for an Einstein-perfect fluid system contained, in addition, volume integrals of the fluid fields, over a spacelike slice stretching between these two surfaces. When applied to the Einstein-perfect fluid system, however, Wald's methods yield restricted results. The reason is that the fluid fields in the Lagrangian of a gravitating perfect fluid are typically nonstationary. We therefore first derive a first law-like relation for an arbitrary Lagrangian metric theory of gravity coupled to arbitrary Lagrangian matter fields, requiring only that the metric field be stationary. This relation includes a volume integral of matter fields over a spacelike slice between the black hole horizon and spatial infinity, and reduces to the first law originally derived by Bardeen, Carter and Hawking when the theory is general relativity coupled to a perfect fluid. We also consider a specific Lagrangian formulation for an isentropic perfect fluid given by Carter, and directly apply Wald's analysis. The resulting first law contains only surface integrals at the black hole horizon and spatial infinity, but this relation is much more restrictive in its allowed fluid configurations and perturbations than that given by Bardeen, Carter and Hawking. In the Appendix, we use the symplectic structure of the Einstein-perfect fluid system to derive a conserved current for perturbations of this system: this current reduces to one derived ab initio for this system by Chandrasekhar and Ferrari.

Vivek Iyer

1996-10-15

145

A Student's Guide to Lagrangians and Hamiltonians

NASA Astrophysics Data System (ADS)

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.

Hamill, Patrick

2013-11-01

146

Permutation Orbifolds in Conformal Field Theories and String Theory

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.

M. Maio

2011-11-03

147

On the Field-Redefinition Theorem in Gravitational Theories

NASA Astrophysics Data System (ADS)

The gravitational sector of classical Lagrangian theories can generally be expressed in the form of a power series L = sqrt {-g} [-1 over 2 kappa -2 R+ sum n=2infty (an Rn+tilde an partial 2 Rn ) ], where kappa 2 is the gravitational coupling and R is the Ricci scalar. By means of a metric field-redefinition gij rightarrow (1+beta R)gij + gamma Rij+ delta RikRjk + . . . , the quadratic terms R2 can be removed completely (due to the Gauss-Bonnet identity) and the cubic and higher-order terms Rn partially, only those terms constructed solely from the Riemann tensor Rijkl remaining invariant. It has been shown by Lawrence, however, that the implementation of this procedure at a specific order n inevitably gives rise to ghosts at the next and higher orders n'ge n+1, in the sense that a term Rn in L is replaced by terms Rn-m(partial 2R)m, for example. Classically, these ghosts may lead to instabilities, and it is therefore necessary to investigate the stability of the theory to linear perturbations, both before and after the metric has been transformed. In the cosmological Friedmann space-time ds2=dt2-a02 e2alpha (t) dx2 which describes the Universe, where t is comoving time and a0 ealpha (t) is the radius function of the three-space dx2, assumed flat, we find, by examining the characteristic equation, that the low-energy solution invariably possesses exponentially growing (and decaying) modes, after carrying out the field redefinition, irrespective of whether such modes were present initially. Therefore, it is not expedient to redefine the metric in this background, which, rather, should be considered as fixed. We discuss the relevance of this result for the heterotic superstring theory, particularly with regard to the vacuum solutions obtained previously from the effective Lagrangian including terms n le 4, and to the terms R2.

Pollock, M. D.

2008-06-01

148

Topics in Effective Field Theory for Lattice QCD

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.

Andre Walker-Loud

2006-08-16

149

Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion

The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introduc- ing a projective system A(n) of observables

M. Dutschand; K. Fredenhagen

2000-01-01

150

Einstein's vierbein field theory of curved space

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.

Jeffrey Yepez

2011-06-10

151

Constitutive Theories for Thermoelastic Solids in Lagrangian Description Using Gibbs Potential

of the constitution of the matter, the second law of thermodynamics, i.e. entropy inequality, must form the basis for all constitutive theories of the deforming matter to ensure thermodynamic equilibrium during the evolution [1, 2]. The entropy inequality expressed...

Mendoza, Yusshy

2012-08-31

152

Large N field theories, string theory and gravity

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

Ofer Aharony; Steven S. Gubser; Juan Maldacena; Hirosi Ooguri; Yaron Oz

2000-01-01

153

Homotopy Classification of Bosonic String Field Theory

NASA Astrophysics Data System (ADS)

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.

Münster, Korbinian; Sachs, Ivo

2014-09-01

154

Homotopy Classification of Bosonic String Field Theory

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.

Korbinian Muenster; Ivo Sachs

2012-08-28

155

Noncommutative Tachyons And String Field Theory

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

Edward Witten

2000-01-01

156

Effective field theory of multi-field inflation a la Weinberg

NASA Astrophysics Data System (ADS)

We generalise Weinberg's effective field theory approach to multiple-field inflation. In addition to standard terms in the Lagrangian we consider terms containing up to the fourth derivative of the scalar fields and the metric. The results illustrate the possible shapes of the interactions which will yield non-Gaussianity. Generally we find that the speed of sound differs from, but is close to unity, however large non-Gaussianities are possible in the multi-field case. The non-Gaussianity of the adiabatic mode and the entropy mode are correlated in shape and amplitude with the amount of the non-Gaussianity depending on the curvature of the classical field path in phase-space. We emphasize that in general the time derivative of adiabatic and entropy perturbations do not invariant due to the shift symmetry. However we find two specific combinations of them are invariant under such a symmetry and these combinations should be employed to construct an effective field theory of multi-field inflation.

Khosravi, Nima

2012-05-01

157

The non-quantum-mechanical interaction of a Dirac magnetic monopole and a point charge through the electromagnetic field is studied. A classical action integral which is multiple-valued is found. Stability of this action integral against variations of the world lines of the point charge and the monopole, and against variations of the electromagnetic potentials, yields the correct Lorentz equations of motion of

T. T. Wu; C. N. Yang

1976-01-01

158

Chiral phase transition for SU(N) gauge theories via an effective Lagrangian approach

We study the chiral phase transition for vectorlike SU(N) gauge theories as a function of the number of quark flavors N{sub f} by making use of an anomaly-induced effective potential. We modify an effective potential of a previous work, suggested for N{sub f}{lt}N, and apply it to larger values of N{sub f} where the phase transition is expected to occur. The new effective potential depends explicitly on the full {beta} function and the anomalous dimension {gamma} of the quark mass operator. By using this potential we argue that chiral symmetry is restored for {gamma}{lt}1. A perturbative computation of {gamma} then leads to an estimate of the critical value N{sub f}{sup c} for the transition. {copyright} {ital 1999} {ital The American Physical Society}

Sannino, F. [Department of Physics, Yale University, New Haven, Connecticut 06520-8120 (United States)] [Department of Physics, Yale University, New Haven, Connecticut 06520-8120 (United States); Schechter, J. [Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States)] [Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States)

1999-09-01

159

Parameterized quantum field theory without Haag's theorem

Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that quantum field theory can be formulated, using an invariant, fifth path parameter in addition to the usual four position parameters, in such a way that Haag's theorem no longer applies, but such that the Dyson perturbation expansion for the sc...

Seidewitz, Ed

2015-01-01

160

Energy-momentum currents in Finsler/Kawaguchi Lagrangian formulation

We reformulate the standard Lagrangian formalism to a reparameterisation invariant Lagrangian formalism by means of Finsler and Kawaguchi geometry. In our formalism, various types of symmetries that appears in theories of physics are expressed geometrically by symmetries of Finsler (Kawaguchi) metric, and the conservation law of energy-momentum is a part of Euler-Lagrange equations. The application to scalar field, Dirac field, electromagnetic field and general relativity are discussed. By this formalism, we try to propose an alternative definition of energy-momentum current of gravity.

Takayoshi Ootsuka; Ryoko Yahagi; Muneyuki Ishida; Erico Tanaka

2014-07-12

161

Decoding the geometry of conformal field theories

To certain geometries, string theory associates conformal field theories. We discuss techniques to perform the reverse procedure: To recover geometrical data from abstractly defined conformal field theories. This is done by introducing appropriate notions of limits of conformal field theories and their degenerations, and by applying techniques from noncommutative geometry. This note is a summary of our work hep-th/0308143 , aimed to be less technical than the original paper, along with some new calculations confirming our interpretation of the rescaled limiting zero mode of the Virasoro field.

Daniel Roggenkamp; Katrin Wendland

2008-03-05

162

Tachyon Condensation: Calculations in String Field Theory

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%.

Pieter-Jan De Smet

2001-09-24

163

Field Theory for Fractional Quantum Hall States

We develop a field theory description of fractional quantum Hall (FQH) states. We show that in the leading approximation in a gradient expansion, Laughlin states are described by a Gaussian free field theory with a background charge which is identified with the anomalous viscosity of the states. The background charge increases the central charge of the corresponding conformal field theory above 1, similar to that of the theory of 2D quantum gravity. Gradient corrections to the Gaussian field theory arising from ultraviolet regularization reflect the gravitational anomaly. They are also related to the Liouville theory of quantum gravity. We show how the gradient expansion of the field action encodes the universal features of the FQH effect beyond that of Hall conductance. This method provides a more transparent and useful alternative for computing the gravitational anomaly and correlation functions of the FQHE in a curved space than the method of iterating the Ward identity employed by the authors in previous papers.

T. Can; M. Laskin; P. Wiegmann

2014-12-30

164

Equivalence Theorem for Lagrangians in Different Dimensions

A proof is given for the observation that the equations of motion for the companion Lagrangian without a square root, subject to some constraints, just reduce to the equations of motion for the companion Lagrangian with a square root in one less dimension. The companion Lagrangian is just an extension of the Klein-Gordon Lagrangian to more fields in order to provide a field description for strings and branes.

L. M. Baker

2000-05-17

165

NASA Astrophysics Data System (ADS)

We present a Lagrangian phase-field method to study the low Reynolds number dynamics of vesicles embedded in a viscous fluid. In contrast to previous approaches, where the field variables are the phase-field and the fluid velocity, here we exploit the fact that the phase-field tracks a material interface to reformulate the problem in terms of the Lagrangian motion of a background medium, containing both the biomembrane and the fluid. We discretize the equations in space with maximum-entropy approximants, carefully shown to perform well in phase-field models of biomembranes in a companion paper. The proposed formulation is variational, lending itself to implicit time-stepping algorithms based on minimization of a time-incremental energy, which are automatically nonlinearly stable. The proposed method deals with two of the major challenges in the numerical treatment of coupled fluid/phase-field models of biomembranes, namely the adaptivity of the grid to resolve the sharp features of the phase-field, and the stiffness of the equations, leading to very small time-steps. In our method, local refinement follows the features of the phase-field as both are advected by the Lagrangian motion, and large time-steps can be robustly chosen in the variational time-stepping algorithm, which also lends itself to time adaptivity. The method is presented in the axisymmetric setting, but it can be directly extended to 3D.

Peco, C.; Rosolen, A.; Arroyo, M.

2013-09-01

166

String field theory vertex from integrability

We propose a framework for computing the (light cone) string field theory vertex in the case when the string worldsheet QFT is a generic integrable theory. The prime example and ultimate goal would be the $AdS_5 \\times S^5$ superstring theory cubic string vertex and the chief application will be to use this framework as a formulation for ${ \\cal N}=4$ SYM theory OPE coefficients valid at any coupling up to wrapping corrections. In this paper we propose integrability axioms for the vertex, illustrate them on the example of the pp-wave string field theory and also uncover similar structures in weak coupling computations of OPE coefficients.

Bajnok, Zoltan

2015-01-01

167

String Field Theory Around the Tachyon Vacuum

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

Leonardo Rastelli; Ashoke Sen; Barton Zwiebach

2000-01-01

168

Quantum Cellular Automata from Lattice Field Theories

We apply the methods of lattice field theories to the quantization of cellular automata. We discuss the quantization of five main categories of cellular automata: bosonic, fermionic, supersymmetric, spin and quantum dot using path integral and operator formalisms of lattice field theories. We show that the quantization of supersymmetric cellular automata is related to recently discussed string bit models of

Michael McGuigan

2003-01-01

169

Numerical Object Oriented Quantum Field Theory Calculations

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.

M. Williams

2009-05-07

170

Descent relations in cubic superstring field theory

NASA Astrophysics Data System (ADS)

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.

Aref'eva, I. Y.; Gorbachev, R.; Medvedev, P. B.; Rychkov, D. V.

2008-01-01

171

Spacetime noncommutative field theories and unitarity

We study the perturbative unitarity of noncommutative scalar field theories. Field theories with spacetime 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

Jaume Gomis; Thomas Mehen

2000-01-01

172

Resonant Tunneling in Scalar Quantum Field Theory

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.

S. -H. Henry Tye; Daniel Wohns

2009-10-06

173

One-loop effective multi-gluon Lagrangian in arbitrary dimensions

We exhibit the one-loop multi-gluon effective Lagrangian in any dimension for a field theory with a quasilocal background, using the background-field formalism. Specific results, including counter terms (up to 12 spacetime dimensions), have been derived, applied to the Yang-Mills theory and found to be in agreement with other string-inspired approaches.

E Rodulfo; R Delbourgo

1997-09-29

174

Soft Theorems from Effective Field Theory

The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate t...

Larkoski, Andrew J; Stewart, Iain W

2014-01-01

175

Aspects of Superconformal Field Theories

NASA Astrophysics Data System (ADS)

Recently, a lot of progress has been made towards understanding the strongly coupled supersymmetric quantum gauge theories. The problem of strong coupling for SU(N) gauge theories can be formulated in two separate regimes of interest, one at finite N and the other at large N in 't Hooft limit. In the first case electric/magnetic duality also called S-duality and in the second, AdS/CFT duality map the strongly coupled problem to a weakly coupled one. Both of the dualities have been well understood in the maximally supersymmetric 4 d gauge theory, the N = 4 super Yang-Mills. In this thesis, as a natural next step, we focus on the strong coupling behavior in N = 2 supersymmetric gauge theories.

Gadde, Abhijit

176

A two-dimensional lagrangian technique for flow field measurement under high dynamic pressure

NASA Astrophysics Data System (ADS)

In this paper, a two-dimensional (2-D) Langrangian technique for flow field measurement under high dynamic pressure is presented, which included a set of experimental device and 2-D Lagrange composite manganin-constantan ring gages. With this kind of gage, the histories of pressure and radial displacement can be measured simultaneously at different Lagrange positions in an axisymmetric shock loading flow field. The technique has some advantages over the 1-D one, such as, simplified loading device, continuously adjustable output pressure, no restriction on sample length and the availability for the study of lateral rarefaction in shock propogation. As a preliminary application, the processes of 2-D shock initiation and attenuation in compacted TNT are measured.

Shi, Huan; Jing, Ding

1990-05-01

177

Perturbative Deformations of Conformal Field Theories Revisited

NASA Astrophysics Data System (ADS)

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.

Kriz, Igor

178

Mass corrections in string theory and lattice field theory

Kaluza-Klein (KK) compactifications of higher-dimensional Yang-Mills theories contain a number of 4-dimensional scalars corresponding to the internal components of the gauge field. While at tree level the scalar zero modes are massless, it is well known that quantum corrections make them massive. We compute these radiative corrections at 1 loop in an effective field theory framework, using the background field method and proper Schwinger-time regularization. In order to clarify the proper treatment of the sum over KK modes in the effective field theory approach, we consider the same problem in two different UV completions of Yang-Mills: string theory and lattice field theory. In both cases, when the compactification radius R is much bigger than the scale of the UV completion (R>>{radical}({alpha}{sup '}), a), we recover a mass renormalization that is independent of the UV scale and agrees with the one derived in the effective field theory approach. These results support the idea that the value of the mass corrections is, in this regime, universal for any UV completion that respects locality and gauge invariance. The string analysis suggests that this property holds also at higher loops. The lattice analysis suggests that the mass of the adjoint scalars appearing in N=2, 4 super Yang-Mills is highly suppressed, even if the lattice regularization breaks all supersymmetries explicitly. This is due to an interplay between the higher-dimensional gauge invariance and the degeneracy of bosonic and fermionic degrees of freedom.

Del Debbio, Luigi; Kerrane, Eoin; Russo, Rodolfo [SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); Centre for Research in String Theory, Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom)

2009-07-15

179

Generating functionals and Lagrangian partial differential equations

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 HamiltonJacobi 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.

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

180

The Lagrangian formulation of the gravitational field equations in general relativity

of the action principle bA = SP qdI1 =O 3n that controls the field equations of geometry. The quantity JQ. is the four-dimensional volume element of Riemannian space-time. POSTKATE V. It will be required that this invariant H be oomposed only of the ~ntal... . Einstein stated that this energy tensor was 7 xk proportional to a differential expression of the second order formed only from the metric tensor a ? . Then following his basic principle 9qk of covariance, he postulated that the differential equation...

Zund, Joe David

2012-06-07

181

Chiral field theories from conifolds

We discuss the geometric engineering and large n transition for an N=1 U(n) chiral gauge theory with one adjoint, one conjugate symmetric, one antisymmetric and eight fundamental chiral multiplets. Our IIB realization involves an orientifold of a non-compact Calabi-Yau A_2 fibration, together with D5-branes wrapping the exceptional curves of its resolution as well as the orientifold fixed locus. We give a detailed discussion of this background and of its relation to the Hanany-Witten realization of the same theory. In particular, we argue that the T-duality relating the two constructions maps the Z_2 orientifold of the Hanany-Witten realization into a Z_4 orientifold in type IIB. We also discuss the related engineering of theories with SO/Sp gauge groups and symmetric or antisymmetric matter.

Landsteiner, K; Tatar, R; Tatar, Radu

2003-01-01

182

Stochastic modeling of Lagrangian accelerations

NASA Astrophysics Data System (ADS)

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.

Reynolds, Andy

2002-11-01

183

Propagators in Lagrangian space

It has been found recently that propagators, e.g. the cross-correlation spectra of the cosmic fields with the initial density field, decay exponentially at large-k in an Eulerian description of the dynamics. We explore here similar quantities defined for a Lagrangian space description. We find that propagators in Lagrangian space do not exhibit the same properties: they are found not to be monotonic functions of time, and to track back the linear growth rate at late time (but with a renormalized amplitude). These results have been obtained with a novel method which we describe alongside. It allows the formal resummation of the same set of diagrams as those that led to the known results in Eulerian space. We provide a tentative explanation for the marked differences seen between the Eulerian and the Lagrangian cases, and we point out the role played by the vorticity degrees of freedom that are specific to the Lagrangian formalism. This provides us with new insights into the late-time behavior of the propagators.

Francis Bernardeau; Patrick Valageas

2008-05-06

184

Unified Field Theories Hitoshi Murayama

Berkeley, CA 94720 Appeared in Encyclopedia of Applied Physics, Vol. 23, 1 (1998) #12;Abstract of electromagnetism and GlashowÂSalamÂWeinberg theory of electroweak forces. Then it describes known four forces in Nature: gravitational, electromagnetic, weak and strong forces, and what their similarities

Murayama, Hitoshi

185

Effective field theories for inclusive B decays

In this thesis, we study inclusive decays of the B meson. These allow one to determine CKM elements precisely and to search for physics beyond the Standard Model. We use the framework of effective field theories, in ...

Lee, Keith S. M. (Keith Seng Mun)

2006-01-01

186

Effective Field Theory for Nuclear Physics

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.

David B. Kaplan

1999-01-01

187

Algebraic conformal quantum field theory in perspective

Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete classifications. The structural insights, analytical methods and constructive tools are expected to be useful also for four-dimensional QFT.

Rehren, Karl-Henning

2015-01-01

188

RATIONAL SYMPLECTIC FIELD THEORY FOR LEGENDRIAN KNOTS

, 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

Ng, Lenny

189

Particle Physics and Introduction to Field Theory

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

T. D. Lee; Sidney Drell

1981-01-01

190

Chiral field theories from conifolds

We discuss the geometric engineering and large n transition for an N=1 U(n) chiral gauge theory with one adjoint, one conjugate symmetric, one antisymmetric and eight fundamental chiral multiplets. Our IIB realization involves an orientifold of a non-compact Calabi-Yau A2 fibration, together with D5-branes wrapping the exceptional curves of its resolution as well as the orientifold fixed locus. We give

Karl Landsteiner; Calin Iuliu Lazaroiu; Radu Tatar

2003-01-01

191

Dark energy or modified gravity? An effective field theory approach

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.

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

192

Lagrangian reduction and the double spherical pendulum

This paper studies the stability and bifurcations of the relative equilibrium of the double spherical pendulum, which has the circle as its symmetry group. The example as well as others with nonabelian symmetry groups, such as the rigid body, illustrate some useful general theory about Lagrangian reduction. In particular, we establish a satisfactory global theory of Lagrangian reduction that is

Jerrold E. Marsden; Juergen Scheurle

1993-01-01

193

Quantum algorithms for quantum field theories.

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

Jordan, Stephen P; Lee, Keith S M; Preskill, John

2012-06-01

194

8.324 Relativistic Quantum Field Theory II, Fall 2005

This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth ...

Zwiebach, Barton

195

Dark matter, Elko fields and Weinberg's quantum field theory formalism

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.

Adam Gillard; Benjamin Martin

2012-05-08

196

Viscosity, Black Holes, and Quantum Field Theory

We review recent progress in applying the AdS/CFT correspondence to finite-temperature field theory. In particular, we show how the hydrodynamic behavior of field theory is reflected in the low-momentum limit of correlation functions computed through a real-time AdS/CFT prescription, which we formulate. We also show how the hydrodynamic modes in field theory correspond to the low-lying quasinormal modes of the AdS black p-brane metric. We provide a proof of the universality of the viscosity/entropy ratio within a class of theories with gravity duals and formulate a viscosity bound conjecture. Possible implications for real systems are mentioned.

D. T. Son; A. O. Starinets

2007-07-11

197

D-branes and string field theory

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 ...

Sigalov, Ilya

2006-01-01

198

Algebras without Involution and Quantum Field Theories

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.

Glenn Eric Johnson

2014-10-01

199

Phase-space quantization of field theory.

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.

Curtright, T.; Zachos, C.

1999-04-20

200

Classification of 2- and 3-FIELD Rational Conformal Field Theories

NASA Astrophysics Data System (ADS)

Using the fact that the fusion algebra of a rational conformal field theory is specified in terms of integers that are related to modular transformation properties, we completely classify 2-field chiral RCFT's. We show that the only possibilities for the non-trivial fusion rule are ? × ? = 1 or ? × ? = 1 + ?. We reduce the 3-field classification to a set of algebraic equations and solve them in a few cases.

Rivlis, Gil

201

"Quantum Field Theory and QCD"

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.

Jaffe, Arthur M.

2006-02-25

202

A general field-covariant formulation of quantum field theory

NASA Astrophysics Data System (ADS)

In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and parameters. Because of this, we cannot write simple identities relating bare and renormalized generating functionals, or generating functionals before and after nonlinear changes of field variables. In this paper we investigate this issue and work out a general field-covariant approach to quantum field theory, which allows us to treat all perturbative changes of field variables, including the relation between bare and renormalized fields, as true changes of variables in the functional integral, under which the functionals Z and W=ln Z behave as scalars. We investigate the relation between composite fields and changes of field variables, and we show that, if J are the sources coupled to the elementary fields, all changes of field variables can be expressed as J-dependent redefinitions of the sources L coupled to the composite fields. We also work out the relation between the renormalization of variable-changes and the renormalization of composite fields. Using our transformation rules it is possible to derive the renormalization of a theory in a new variable frame from the renormalization in the old variable frame, without having to calculate it anew. We define several approaches, useful for different purposes, in particular a linear approach where all variable changes are described as linear source redefinitions. We include a number of explicit examples.

Anselmi, Damiano

2013-03-01

203

Lagrangian postprocessing of computational hemodynamics.

Recent advances in imaging, modeling, and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries, and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows. PMID:25059889

Shadden, Shawn C; Arzani, Amirhossein

2015-01-01

204

New Cosmological Signatures from Double Field Theory

In cosmology, it has been a long-standing problem to establish a \\emph{parameter insensitive} evolution from an anisotropic phase to an isotropic phase. On the other hand, it is of great importance to construct a theory having extra dimensions as its intrinsic ingredients. We show that these two problems are closely related and can naturally be solved simultaneously in double field theory cosmology. Our derivations are based on general arguments without any fine-tuning parameters. In addition, We find that when we begin with FRW metric, the full spacetime metric of DFT totally agrees with \\emph{Kaluza-Klein theory}. There is a visible and invisible dimension exchange between the pre- and post-big bangs. Our results indicate that double field theory has profound physical consequences and the continuous $O\\left(D,D\\right)$ is a very fundamental symmetry. This observation reinforces the viewpoint that symmetries dictate physics.

Houwen Wu; Haitang Yang

2014-05-21

205

Lattice Field Theory Methods in Modern Biophysics

An effective field theory exists describing a very large class of biophysically interesting Coulomb gas systems: the lowest order (mean-field) version of this theory takes the form of a generalized Poisson-Boltzmann theory. Interaction terms depend on details (finite-size effects, multipole properties, etc). Convergence of the loop expansion holds only if mutual interactions of mobile charges are small compared to their interaction with the fixed-charge environment, which is frequently not the case. Problems with the strongly- coupled effective theory can be circumvented with an alternative local lattice formulation, with real positive action. In realistic situations, with variable dielectric, a determinant of the Poisson operator must be inserted to generate correct electrostatics. Methods adopted from unquenched lattice QCD do this very efficiently.

Anthony Duncan

2006-09-28

206

Tachyon condensation in superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the D-braneanti-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 WessZuminoWitten-like open superstring field theory free of contact term divergences and recently shown to give 60% of the vacuum energy by

Nathan Berkovits; Ashoke Sen; Barton Zwiebach

2000-01-01

207

Neutrix Calculus and Finite Quantum Field Theory

In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT,obtaining finite renormalizations. While none of the physically measurable results in renormalizable QFT is changed, quantum gravity is rendered more manageable in the neutrix framework.

Y. Jack Ng; H. van Dam

2005-04-04

208

a Nonassociative Quaternion Scalar Field Theory

NASA Astrophysics Data System (ADS)

A nonassociative Groenewold-Moyal (GM) plane is constructed using quaternion-valued function algebras. The symmetrized multiparticle states, the scalar product, the annihilation/creation algebra and the formulation in terms of a Hopf algebra are also developed. Nonassociative quantum algebras in terms of position and momentum operators are given as the simplest examples of a framework whose applications may involve string theory and nonlinear quantum field theory.

Giardino, Sergio; Teotônio-Sobrinho, Paulo

2013-11-01

209

The amplitude of quantum field theory

General properties of the transition amplitude in axiomatic quantum field theory are discussed. Bogolyubov's axiomatic method is chosen as the variant of the theory. The axioms of this method are analyzed. In particular, the significance of the off-shell extension and of the various forms of the causality condition are examined. A complete proof is given of the existence of a single analytic function whose boundary values are the amplitudes of all channels of a process with given particle number.

Medvedev, B.V. (Institute of Experimental and Theoretical Physics, Moscow (SU)); Pavlov, V.P.; Polivanov, M.K. (V. A. Steklov Mathematics Institute, USSR Academy of Sciences (USSR)); Sukhanov, A.D. (All-Union Correspondence Institute of Textile and Light Industries, Moscow (SU))

1989-05-01

210

Tachyon condensation in string field theory

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

Ashoke Sen; Barton Zwiebach

2000-01-01

211

Regge behavior in effective field theory

NASA Astrophysics Data System (ADS)

We derive the Regge behavior for the forward scattering amplitude in scalar field theory using the method of regions. We find that the leading Regge behavior to all orders can be obtained. Regge physics emerges from a kinematic region that involves the overlap of several modes, so that a careful treatment of the overlap regions is important. The most consistent and efficient approach utilizes graphs containing collinear, anticollinear and Glauber modes, or modes of soft collinear effective theory with Glauber gluons (SCETG ).

Donoghue, John F.; El-Menoufi, Basem Kamal; Ovanesyan, Grigory

2014-11-01

212

Topological field theory and rational curves

We analyze the quantum field theory corresponding to a string propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear ?-model and the structure of rational curves on the Calabi-Yau manifold. We study in detail the case of the world-sheet of the string being mapped to a multiple cover of an isolated rational curve

Paul S. Aspinwall; David R. Morrison

1993-01-01

213

Multisymplectic effective General Boundary Field Theory

The transfer matrix in lattice field theory connects the covariant and the initial data frameworks; in spin foam models, it can be written as a composition of elementary cellular amplitudes/propagators. We present a framework for discrete spacetime classical field theory in which solutions to the field equations over elementary spacetime cells may be amalgamated if they satisfy simple gluing conditions matching the composition rules of cellular amplitudes in spin foam models. Furthermore, the formalism is endowed with a multisymplectic structure responsible for local conservation laws. Some models within our framework are effective theories modeling a system at a given scale. Our framework allows us to study coarse graining and the continuum limit.

Mona Arjang; José A. Zapata

2014-03-01

214

Dual PT-Symmetric Quantum Field Theories

Some quantum field theories described by non-Hermitian Hamiltonians are investigated. It is shown that for the case of a free fermion field theory with a $\\gamma_5$ mass term the Hamiltonian is $\\cal PT$-symmetric. Depending on the mass parameter this symmetry may be either broken or unbroken. When the $\\cal PT$ symmetry is unbroken, the spectrum of the quantum field theory is real. For the $\\cal PT$-symmetric version of the massive Thirring model in two-dimensional space-time, which is dual to the $\\cal PT$-symmetric scalar Sine-Gordon model, an exact construction of the $\\cal C$ operator is given. It is shown that the $\\cal PT$-symmetric massive Thirring and Sine-Gordon models are equivalent to the conventional Hermitian massive Thirring and Sine-Gordon models with appropriately shifted masses.

Carl M. Bender; H. F. Jones; R. J. Rivers

2005-08-15

215

A multisymplectic unified formalism for second-order classical field theories

We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified Lagrangian-Hamiltonian formalism to these kinds of systems. Our model allows us to overcome all the ambiguities inherent to these theories. It therefore provides a straightforward and simple way to define the Poincar\\'{e}-Cartan form and clarifies the construction of the Legendre map (univocally obtained as a consequence of the constraint algorithm). Likewise, it removes the undesirable arbitrariness in the solutions to the field equations, which are analyzed in-depth, and written in terms of holonomic sections and multivector fields. Our treatment therefore completes previous attempt to achieve this aim. The formulation is applied to describing some physical examples; in particular, to giving another alternative multisymplectic description of the Korteweg-de Vries equation.

Pedro D. Prieto-Martínez; Narciso Román-Roy

2014-02-17

216

A New World Sheet Field Theory

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.

Korkut Bardakci

2008-08-21

217

Non-exponential decay in Quantum Mechanics and Quantum Field Theory

NASA Astrophysics Data System (ADS)

We describe some salient features as well as some recent developments concerning short-time deviations from the exponential decay law in the context of Quantum Mechanics by using the Lee Hamiltonian approach and Quantum Field Theory by using relativistic Lagrangians. In particular, the case in which two decay channels are present is analyzed: the ratio of decay probability densities, which is a constant equal to the ratio of decay widths in the exponential limit, shows in general sizable fluctuations which persist also at long times.

Giacosa, Francesco

2014-10-01

218

Extending the standard model effective field theory with the complete set of dimension-7 operators

NASA Astrophysics Data System (ADS)

We present a complete list of the independent dimension-7 operators that are constructed using the standard model degrees of freedom and are invariant under the standard model gauge group. This list contains only 20 independent operators, far fewer than the 63 operators available at dimension 6. All of these dimension-7 operators contain fermions and violate lepton number, and 7 of the 20 violate baryon number as well. This result extends the standard model effective field theory and allows a more detailed exploration of the structure and properties of possible deformations from the standard model Lagrangian.

Lehman, Landon

2014-12-01

219

Effective Field Theory for Long Strings

In previous work we used magnetic SU(N) gauge theory with adjoint representation Higgs scalars to describe the long distance quark-antiquark interaction in pure Yang-Mills theory, and later to obtain an effective string theory. The empirically determined parameters of the non-Abelian effective theory yielded $Z_N$ flux tubes resembling those of the Abelian Higgs model with Landau-Ginzburg parameter equal to $ 1/\\sqrt{2}$, corresponding to a superconductor on the border between type I and type II. However, the physical significance of the differences between the Abelian and the $Z_N$ vortices was not elucidated and no principle was found to fix the value of the 'Landau-Ginzburg parameter' $\\kappa$ of the non-Abelian theory determining the structure of the $Z_N$ vortices. Here we reexamine this point of view. We propose a consistency condition on $Z_N$ vortices underlying a confining string. This fixes the value of $\\kappa$. The transverse distribution of pressure $p(r)$ in the resulting $Z_N$ flux tubes provides a physical picture of these vortices which differs essentially from that of the vortices of the Abelian Higgs model. We speculate that this general picture is valid independent of the details of the effective magnetic gauge theory from which it was obtained. Long wavelength fluctuations of the axis of the $Z_N$ vortices lead from an effective field theory to an effective string theory with the Nambu-Goto action. This effective string theory depends on a single parameter, the string tension $\\sigma$. In contrast, the effective field theory has a second parameter, the intrinsic width 1/M of the flux tube.

M. Baker

2013-01-18

220

Topics in quantum field theory and cosmology

This thesis contains a study of topics in quantum field theory and cosmology in the context of the new inflationary universe scenario. It presents a review of the quantum field theory methods used in the new cosmological models. The following chapters are a detailed study of energy density fluctuations in the early universe. Hawking radiation is derived as the source of initial perturbations in two complementary ways. The following section presents a new gauge invariant framework to study the growth of fluctuations outside the horizon. This framework is applied to the new inflationary universe in the final chapter. The introduction gives a brief outline of the new cosmological models.

Brandenberger, R.H.

1983-01-01

221

On the theory of gravitation field

We construct a general relativity formula for the law of gravity for material bodies. The formula contains three numeric parameters that are to be determined experimentally. If they are chosen from symmetry considerations, then the theory that appears is close to the theory of electrodynamics: the gravitational field is given by two vector fields, one can write the energy-momentum tensor, we give an answer on the question what a gravitational wave is. Going to infinity, this wave carries with it the negative energy.

N. N. Chaus

1999-03-12

222

Effective theories of single field inflation when heavy fields matter

NASA Astrophysics Data System (ADS)

We compute the low energy effective field theory (EFT) expansion for single-field inflationary models that descend from a parent theory containing multiple other scalar fields. By assuming that all other degrees of freedom in the parent theory are sufficiently massive relative to the inflaton, it is possible to derive an EFT valid to arbitrary order in perturbations, provided certain generalized adiabaticity conditions are respected. These conditions permit a consistent low energy EFT description even when the inflaton deviates off its adiabatic minimum along its slowly rolling trajectory. By generalizing the formalism that identifies the adiabatic mode with the Goldstone boson of this spontaneously broken time translational symmetry prior to the integration of the heavy fields, we show that this invariance of the parent theory dictates the entire non-perturbative structure of the descendent EFT. The couplings of this theory can be written entirely in terms of the reduced speed of sound of adiabatic perturbations. The resulting operator expansion is distinguishable from that of other scenarios, such as standard single inflation or DBI inflation. In particular, we re-derive how certain operators can become transiently strongly coupled along the inflaton trajectory, consistent with slow-roll and the validity of the EFT expansion, imprinting features in the primordial power spectrum, and we deduce the relevant cubic operators that imply distinct signatures in the primordial bispectrum which may soon be constrained by observations.

Achúcarro, Ana; Gong, Jinn-Ouk; Hardeman, Sjoerd; Palma, Gonzalo A.; Patil, Subodh P.

2012-05-01

223

Coherent states formulation of polymer field theory

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first direct numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards well-known auxiliary-field (AF) framework, the CS formulation does not contain an embedded nonlinear, non-local, implicit functional of the auxiliary fields, and the action of the field theory has a fully explicit, semi-local, and finite-order polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF-CL simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.

Man, Xingkun; Villet, Michael C. [Department of Chemical Engineering, University of California, Santa Barbara, California 93106 (United States) [Department of Chemical Engineering, University of California, Santa Barbara, California 93106 (United States); Materials Research Laboratory, University of California, Santa Barbara, California 93106 (United States); Delaney, Kris T. [Materials Research Laboratory, University of California, Santa Barbara, California 93106 (United States)] [Materials Research Laboratory, University of California, Santa Barbara, California 93106 (United States); Orland, Henri [Institut de Physique Théorique, CE-Saclay, CEA, F-91191 Gif-sur-Yvette Cedex (France)] [Institut de Physique Théorique, CE-Saclay, CEA, F-91191 Gif-sur-Yvette Cedex (France); Fredrickson, Glenn H., E-mail: ghf@mrl.ucsb.edu [Department of Chemical Engineering, University of California, Santa Barbara, California 93106 (United States); Materials Research Laboratory, University of California, Santa Barbara, California 93106 (United States); Materials Department, University of California, Santa Barbara, California 93106 (United States)

2014-01-14

224

Astrophysical data analysis with information field theory

NASA Astrophysics Data System (ADS)

Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.

Enßlin, Torsten

2014-12-01

225

Astrophysical data analysis with information field theory

Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.

Enßlin, Torsten

2014-01-01

226

Noncommutative Geometry in M-Theory and Conformal Field Theory

In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U{sub q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun{sub q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.

Morariu, Bogdan

1999-05-01

227

Symmetry analysis for anisotropic field theories

The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.

Parra, Lorena; Vergara, J. David [Instituto de Ciencias Nucleares, UNAM, Circuito Exterior s/n, Ciudad Universitaria. Delg. Coyoacan. C.P. 04510 Mexico DF (Mexico)

2012-08-24

228

The Mean-Field Flux Pinning Theory

NASA Astrophysics Data System (ADS)

We develop the Mean-Field Flux Pinning Theory, designed to model the flux line lattice (FLL) as it interacts with itself, the flux pinning centers and the geometry of the superconductor. Like other mean-field theories, the mean-field flux pinning theory does not attempt to model the FLL completely. Instead, it utilizes a simplified model for the FLL, termed the mean-field FLL, in which the FLL is modelled as a continuous vector field rather than as discrete fluxons as in other theories. By so doing, the interactions of the FLL are greatly simplified and more easily modelled. One application of the mean-field flux pinning theory is to predict J_{c} from microstructural data, which we use to determine the optimal Nb-Ti microstructures with (1) alpha -Ti pinning centers and (2) Nb pinning centers. The microstructure is modelled on a grid in which the local values of T_{c} and kappa reflect the spatial distribution of the pinning centers and the superconductor. Using this model, we solve the G-L equations and calculate the pinning potential defined as the vortex free energy as a function of position. We conclude that the ideal Nb-Ti microstructure with alpha-Ti pinning centers would require 40 volume percent of alpha -Ti and have 6nm thick pinning centers. In the Nb pinning center case, the ideal microstructure requires 50 volume percent of Nb and would have 6nm pinning centers. Another application for the mean-field flux pinning theory is to model the FLL as it interacts with the penetrating magnetic fields within lambda of the superconducting surface. Using this theory, we study the effects of sample geometry on the FLL and J _{c} for the thin film geometry. We find that the FLL becomes increasingly distorted as the film thickness is reduced and that J_{c } increases sharply for dimensions less that lambda. These predictions are experimentally evaluated in Nb-Ti thin films. Our results show that J_{c} values as high as 1/3 of J_{d} and a strong orientational dependence J_{c} is possible as a result of the geometry.

Stejic, George

229

Light field integration in SUGRA theories

NASA Astrophysics Data System (ADS)

We revisit the integration of fields in 𝒩 = 1 Supergravity with the requirement that the effective theory has a reliable two-derivative supersymmetric description. In particular, we study, in a supersymmetric manifest way, the situation where the fields that are mapped out have masses comparable to the Supersymmetry breaking scale and masses of the remaining fields. We find that as long as one stands in regions of the field configuration space where the analytic continuation to superspace of the F-flatness conditions be reliable equations of motion for the fields that are being mapped out, and provided their solutions are stable regardless the dynamics of the remaining fields, such a two-derivative description is a reliable truncation of the full effective theory. The study is mainly focused to models with two chiral sectors, H and L, described by a Kähler invariant function with schematic dependencies of the form G = GH(H, \\bar H)+GL(L, \\bar L), which leads to a nearly decoupled theory that allows the previous requirements to be easily satisfied in a consistent way. Interestingly, enough for the matters of our study, this kind of models present a scenario that is as safe as the one presented in sequestered models. It is also possible to allow gauge symmetries as long as these appear also factorized in hidden and visible sectors. Then, the integration of the hidden vector superfields is compulsory and proceeds reliably through the D-flatness condition analytically continued to superspace.

Gallego, Diego

2015-01-01

230

Continuous wavelet transform in quantum field theory

NASA Astrophysics Data System (ADS)

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).

Altaisky, M. V.; Kaputkina, N. E.

2013-07-01

231

Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory

NASA Astrophysics Data System (ADS)

This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.

Maroun, Michael Anthony

232

Cross Sections From Scalar Field Theory

NASA Technical Reports Server (NTRS)

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.

Norbury, John W.; Dick, Frank; Norman, Ryan B.; Nasto, Rachel

2008-01-01

233

Coadjoint Orbits and Conformal Field Theory

This thesis describes a new approach to conformal field theory. This approach combines the method of coadjoint orbits with resolutions and chiral vertex operators to give a construction of the correlation functions of conformal field theories in terms of geometrically defined objects. Explicit formulae are given for representations of Virasoro and affine algebras in terms of a local gauge choice on the line bundle associated with geometric quantization of a given coadjoint orbit; these formulae define a new set of explicit bosonic realizations of these algebras. The coadjoint orbit realizations take the form of dual Verma modules, making it possible to avoid the technical difficulties associated with the two-sided resolutions which arise from Feigin-Fuchs and Wakimoto realizations. Formulae are given for screening and intertwining operators on the coadjoint orbit representations. Chiral vertex operators between Virasoro modules are constructed, and related directly to Virasoro algebra generators in certain cases. From the point of view taken in this thesis, vertex operators have a geometric interpretation as differential operators taking sections of one line bundle to sections of another. A suggestion is made that by connecting this description with recent work deriving field theory actions from coadjoint orbits, a deeper understanding of the geometry of conformal field theory might be achieved.

Washington Taylor IV

1993-10-11

234

CONSTRUCTIVE QUANTUM FIELD THEORY ARTHUR JAFFE

electrodynamics. These effects deviated numerically from the predictions arising from equations that describe a fixed number of particles, so they were accurate tests of the quantum field hypothesis. Today-perturbative level. Doubts about quantum electrodynamics or scalar meson theory were raised early by Dyson and Landau

Jaffe, Arthur

235

Bound States in Quantum Field Theory

The relativistic two-body equation of Bethe and Salpeter is derived from field theory. It is shown that the Feynman two-body kernel may be written as a sum of wave functions over the states of the system. These wave functions depend exponentially on the energies of the states to which they correspond and therefore provide a means of calculating energy levels

Murray Gell-Mann; Francis Low

1951-01-01

236

Quantum Field Theory, Black Holes and Holography

These notes are an expanded version of lectures given at the Croatian School on Black Holes at Trpanj, June 21-25, 2010. The aim is to provide a practical introduction to quantum field theory in curved spacetime and related black hole physics, with AdS/CFT as the loose motivation.

Chethan Krishnan

2010-11-26

237

Strongly Coupled Chameleon Fields: New Horizons in Scalar Field Theory

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.

David F. Mota; Douglas J. Shaw

2006-09-16

238

Monte Carlo approaches to effective field theories

In this paper, we explore the application of continuum Monte Carlo methods to effective field theory models. Effective field theories, in this context, are those in which a Fock space decomposition of the state is useful. These problems arise both in nuclear and condensed matter physica. In nuclear physics, much work has been done on effective field theories of mesons and baryons. While the theories are not fundamental, they should be able to describe nuclear properties at low energy and momentum scales. After describing the methods, we solve two simple scalar field theory problems; the polaron and two nucleons interacting through scalar meson exchange. The methods presented here are rather straightforward extensions of methods used to solve quantum mechanics problems. Monte Carlo methods are used to avoid the truncation inherent in a Tamm-Dancoff approach and its associated difficulties. Nevertheless, the methods will be most valuable when the Fock space decomposition of the states is useful. Hence, while they are not intended for ab initio studies of QCD, they may prove valuable in studies of light nuclei, or for systems of interacting electrons and phonons. In these problems a Fock space decomposition can be used to reduce the number of degrees of freedom and to retain the rotational symmetries exactly. The problems we address here are comparatively simple, but offer useful initial tests of the method. We present results for the polaron and two non-relativistic nucleons interacting through scalar meson exchange. In each case, it is possible to integrate out the boson degrees of freedom exactly, and obtain a retarded form of the action that depends only upon the fermion paths. Here we keep the explicit bosons, though, since we would like to retain information about the boson components of the states and it will be necessary to keep these components in order to treat non-scalar of interacting bosonic fields.

Carlson, J. (Los Alamos National Lab., NM (United States)); Schmidt, K.E. (Arizona State Univ., Tempe, AZ (United States). Dept. of Physics)

1991-01-01

239

Symmetry aspects of nonholonomic field theories

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.

J. Vankerschaver; D. Martin de Diego

2007-12-14

240

A gauge field theory of spacetime based on the de Sitter group

NASA Astrophysics Data System (ADS)

A new theory of spacetime is proposed in which translations are considered as a part of the de Sitter gauge group. The theory is built along the general principles of classical gauge field theories, which are outlined. Applications of gauge principles to linear and affine connections are also given in order to make the presentation self-sufficient. A de Sitter invariant Lagrangian is constructed, which yields approximately Einstein's vacuum equations when it is subjected to variation with respect to gauge potentials and the result expressed in a specific gauge class. As a difference from the usual use of de Sitter groups, the radius of its translations must be small in the present approach, which probably has the meaning of an elementary subatomic length. The solution of the equations describing flat spacetime is not the trivial zero-curvature connection of the conventional approach.

Smrz, P. K.

1980-04-01

241

Quantum stability of chameleon field theories.

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

Upadhye, Amol; Hu, Wayne; Khoury, Justin

2012-07-27

242

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.

Saririan, K.

1997-05-01

243

Effective field theory of gravity for extended objects

NASA Astrophysics Data System (ADS)

Using effective field theory (EFT) methods we present a Lagrangian formalism which describes the dynamics of nonrelativistic extended objects coupled to gravity. The formalism is relevant to understanding the gravitational radiation power spectra emitted by binary star systems, an important class of candidate signals for gravitational wave observatories such as LIGO or VIRGO. The EFT allows for a clean separation of the three relevant scales: rs, the size of the compact objects, r, the orbital radius, and r/v, the wavelength of the physical radiation (where the velocity v is the expansion parameter). In the EFT, radiation is systematically included in the v expansion without the need to separate integrals into near zones and radiation zones. Using the EFT, we show that the renormalization of ultraviolet divergences which arise at v6 in post-Newtonian (PN) calculations requires the presence of two nonminimal worldline gravitational couplings linear in the Ricci curvature. However, these operators can be removed by a redefinition of the metric tensor, so that the divergences arising at v6 have no physically observable effect. Because in the EFT finite size features are encoded in the coefficients of nonminimal couplings, this implies a simple proof of the decoupling of internal structure for spinless objects to at least order v6. Neglecting absorptive effects, we find that the power counting rules of the EFT indicate that the next set of short distance operators, which are quadratic in the curvature and are associated with tidal deformations, does not play a role until order v10. These operators, which encapsulate finite size properties of the sources, have coefficients that can be fixed by a matching calculation. By including the most general set of such operators, the EFT allows one to work within a point-particle theory to arbitrary orders in v.

Goldberger, Walter D.; Rothstein, Ira Z.

2006-05-01

244

On the Lagrangian theory for rotating charge in the Maxwell field

NASA Astrophysics Data System (ADS)

We justify the Hamilton least action principle for the Maxwell-Lorentz equations coupled with the equations of motion of Abraham's rotating extended electron. The main novelty in the proof is the application of the variational Poincaré equations on the Lie group SO (3).

Imaykin, Valeriy; Komech, Alexander; Spohn, Herbert

2015-01-01

245

Conformal field theories in a periodic potential: Results from holography and field theory

We study (2+1)-dimensional conformal field theories (CFTs) with a globally conserved U(1) charge, placed in a chemical potential which is periodically modulated along the spatial direction x with zero average: ?(x)=V?cos(kx). ...

Chesler, Paul

246

A master functional for quantum field theory

NASA Astrophysics Data System (ADS)

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.

Anselmi, Damiano

2013-04-01

247

Relative entropies in conformal field theory.

Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance. PMID:25126908

Lashkari, Nima

2014-08-01

248

Nuclear effective field theory on the lattice

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.

Hermann Krebs; Bugra Borasoy; Evgeny Epelbaum; Dean Lee; Ulf-G. Meiß ner

2008-10-01

249

Vortex operators in gauge field theories

Several related aspects of the 't Hooft vortex operator are studied. The current picture of the vacuum of quantum chromodynamics, the idea of dual field theories, and the idea of the vortex operator are reviewed first. The Abelian vortex operator written in terms of elementary fields and the calculation of its Green's functions are considered. A two-dimensional solvable model of a Dirac string is presented. The expression of the Green's functions more neatly in terms of Wu and Yang's geometrical idea of sections is addressed. The renormalization of the Green's functions of two kinds of Abelian looplike operators, the Wilson loop and the vortex operator, is studied; for both operators only an overall multiplicative renormalization is needed. In the case of the vortex this involves a surprising cancellation. Next, the dependence of the Green's functions of the Wilson and 't Hooft operators on the nature of the vacuum is discussed. The cluster properties of the Green's functions are emphasized. It is seen that the vortex operator in a massive Abelian theory always has surface-like clustering. The form of Green's functions in terms of Feynman graphs is the same in Higgs and symmetric phases; the difference appears in the sum over all tadpole trees. Finally, systems having fields in the fundamental representation are considered. When these fields enter only weakly into the dynamics, a vortex-like operator is anticipated. Any such operator can no longer be local looplike, but must have commutators at long range. A U(1) lattice gauge theory with two matter fields, one singly charged (fundamental) and one doubly charged (adjoint), is examined. When the fundamental field is weakly coupled, the expected phase transitions are found. When it is strongly coupled, the operator still appears to be a good order parameter, a discontinuous change in its behavior leads to a new phase transition. 18 figures.

Polchinski, J.

1980-07-01

250

Advances in mean-field dynamo theories

NASA Astrophysics Data System (ADS)

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.

Pipin, V. V.

2013-07-01

251

Graphene as a Lattice Field Theory

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.

Simon Hands; Wes Armour; Costas Strouthos

2015-01-08

252

Graphene as a Lattice Field Theory

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.

Hands, Simon; Strouthos, Costas

2015-01-01

253

On Multi-Point Liouville Field Theory

NASA Astrophysics Data System (ADS)

In many cases, the classical or semi-classical Liouville field theory appears in the form of Fuchsian or Riemann differential equations whose solutions cannot be simply found, or atleast require a comprehensive knowledge on analytical techniques of differential equations of mathematical physics. Here, instead of other cumbersome methodologies such as treating with the Heun functions, we use the quasi-exact ansatz approach and thereby solve the so-called resulting two- and three-point differential equations in a very simple manner. We apply the approach to two recent papers in the field.

Zarrinkamar, S.; Hassanabadi, H.; Rajabi, A. A.

2013-11-01

254

Field Theories of Topological Random Walks

In this work we derive certain topological theories of transverse vector fields whose amplitudes reproduce topological invariants involving the interactions among the trajectories of three and four random walks. This result is applied to the construction of a field theoretical model which describes the statistical mechanics of an arbitrary number of topologically linked polymers in the context of the analytical approach of Edwards. With respect to previous attempts, our approach is very general, as it can treat a system involving an arbitrary number of polymers and the topological states are not only specified by the Gauss linking number, but also by higher order topological invariants.

Franco Ferrari; Ignazio Lazzizzera

1999-06-14

255

On cosmic inflation in vector field theories

NASA Astrophysics Data System (ADS)

We investigate the longitudinal ghost issue in Abelian vector inflation. It turns out that, within the class of Lorentz-invariant vector field theories with three degrees of freedom and without any extra (scalar) fields, the possibilities are essentially exhausted by the classical solution due to Larry Ford with an extremely flat potential which does not feel the fast roll of its argument. And, moreover, one needs to fulfill an extra condition on that potential in order to avoid severe gradient instability. At the same time, some Lorentz-violating modifications are worth exploring.

Golovnev, Alexey

2011-12-01

256

Scalar Field Theories with Polynomial Shift Symmetries

We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree $P$ in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree $P$, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree $P$? To answer this (essen...

Griffin, Tom; Horava, Petr; Yan, Ziqi

2014-01-01

257

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

258

The Global Approach to Quantum Field Theory

Bryce Seligman DeWitt (19232004), a friend and mentor to many, was a towering figure in the development of the quantum theories of gravity and gauge fields. To appreciate his uniqueness, one must recall the history through which he lived. From DeWitt's birth date through 1965, general relativity (GR) was considered to have so few empirically testable predictions that its practitioners

S A Fulling

2006-01-01

259

Loop quantum cosmology from group field theory

NASA Astrophysics Data System (ADS)

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.

Calcagni, Gianluca

2014-09-01

260

Lagrangian fronts in the ocean

NASA Astrophysics Data System (ADS)

We introduce the concept of Lagrangian fronts (LFs) in the ocean and describe their importance for analyzing water mixing and transport and the specific features and differences from hydrological fronts. A method of calculating LFs in a given velocity field is proposed. Based on altimeter velocity fields from AVISO data in the northwestern Pacific, we calculate the Lagrangian synoptic maps and identify LFs of different spatial and temporal scales. Using statistical analysis of saury catches in different years according to the Goskomrybolovstvo (State Fisheries Committee of the Russian Federation), we show that LFs can serve as good indicators of places that are favorable for fishing.

Prants, S. V.; Budyansky, M. V.; Uleysky, M. Yu.

2014-05-01

261

Lagrangian continuum dynamics in ALEGRA.

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.

Wong, Michael K. W.; Love, Edward

2007-12-01

262

Adaptive Perturbation Theory: Quantum Mechanics and Field Theory

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, H, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. In this talk I will introduce the method in the context of the pure anharmonic oscillator and then apply it to the case of tunneling between symmetric minima. After that, I will show how this method can be applied to field theory. In that discussion I will show how one can non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.

Weinstein, Marvin; /SLAC

2005-10-19

263

Spaces of Conformal Theories and String Field Theory

NASA Astrophysics Data System (ADS)

The problems studied in this thesis were motivated by (a) the program of constructing closed bosonic string field theories (CSFTs), and (b) the issue of background independence in string field theory. Certain minimal area metrics on punctured Riemann surfaces can be used to construct a CSFT, if among other things, these metrics are flat around punctures. The theorem proved in Chapter 2 shows that a minimal area metric is flat around punctures, if there exist neighbourhoods of the punctures that are uniquely foliated by the saturating curves of the metric. Since such foliation was expected the theorem moved one closer to verifying that CSFTs can be constructed. Once CSFTs were in hand, background dependence of the string field action engaged interest. This led to a study of covariant derivatives (interchangeably called connections) on the bundle of states of a space of CFTs, the results of which are presented in Chapter 3. The study clarified the general framework for examining spaces of CFTs and this led (a) to the characterization of covariant derivatives by operator forms omega^epsilon, and (b) to the canonical connection types, Gamma ^{D}, c and | c . One expects to be able to (through use of CFT data) infer, from knowledge of an omega^ epsilon characterizing a connection Gamma, most of the interesting properties and off shoots of Gamma. Things fall short of this expectation, somewhat. The shortfall is analyzed with regard to connection coefficients in an eigenbasis of L_0 and | L_0, BPZ metric compatibility, pull backs of connections to the base and curvature. For a test of the ideas in Chapter 3, toroidally compactified theories are an accessible playground and Chapter 4 recounts a visit to these parts. The highpoints are, that nabla ^{KZ}, a connection that arises naturally in such theory spaces, is a Gamma ^{D} type connection with D the unit disc and that nabla^{KZ } becomes the Zamolodchikov connection when pulled back to the base. Chapter 5 is concerned with the perturbative construction of a CFT in the state space of another. The use of parallel transport yields, as expected, a canonical construction manifestly free of divergences. From this perturbative construction, we extract necessary and sufficient conditions for existence of an extension to a theory space. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617 -253-5668; Fax 617-253-1690.).

Kirshnan, Ranganathan

264

The clebsch potential approach to fluid lagrangians

The clebsch potential approach to fluid lagrangians is developed in order to establish contact with other approaches to fluids. Three variants of the perfect fluid approach are looked at. The first is an explicit linear lagrangian constructed directly from the clebsch potentials, this has fixed equation of state and explicit expression for the pressure but is less general than a perfect fluid. The second is lagrangians more general than that of a perfect fluid which are constructed from higher powers of the comoving vector. The third is lagrangians depending on two vector fields which can represent both density flow and entropy flow.

Mark D. Roberts

2009-10-19

265

A novel string field theory solving string theory by liberating left and right movers

NASA Astrophysics Data System (ADS)

We put forward ideas to a novel string field theory based on making some "objects" that essentially describe "liberated" left- and right- mover fields ( ? + ?) and ( ? - ?) on the string. Our novel string field theory is completely definitely different from any other string theory in as far as a "null set" of information in the string field theory Fock space has been removed relatively, to the usual string field theories. So our theory is definitely new. The main progress is that we manage to make our novel string field theory provide the correct mass square spectrum for the string. We finally suggest how to obtain the Veneziano amplitude in our model.

Nielsen, Holger B.; Ninomiya, Masao

2014-05-01

266

Scalar Field Theories with Polynomial Shift Symmetries

We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree $P$ in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree $P$, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree $P$? To answer this (essentially cohomological) question, we develop a new graph-theoretical technique, and use it to prove several classification theorems. First, in the special case of $P=1$ (essentially equivalent to Galileons), we reproduce the known Galileon $N$-point invariants, and find their novel interpretation in terms of graph theory, as an equal-weight sum over all labeled trees with $N$ vertices. Then we extend the classification to $P>1$ and find a whole host of new invariants, including those that represent the most relevant (or least irrelevant) deformations of the corresponding Gaussian fixed points, and we study their uniqueness.

Tom Griffin; Kevin T. Grosvenor; Petr Horava; Ziqi Yan

2014-12-02

267

Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean

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.

F. J. Beron-Vera; M. J. Olascoaga; G. Haller; M. Farazmand; J. Trinanes; Y. Wang

2014-08-27

268

The treatment of exact conservation laws in Lagrangian gauge theories constitutes the main axis of the first part of the thesis. The formalism is developed as a self-consistent theory but is inspired by earlier works, mainly by cohomological results, covariant phase space methods and by the Hamiltonian formalism. The thermodynamical properties of black holes, especially the first law, are studied in a general geometrical setting and are worked out for several black objects: black holes, strings and rings. Also, the geometrical and thermodynamical properties of a new family of black holes with closed timelike curves in three dimensions are described. The second part of the thesis is the natural generalization of the first part to asymptotic analyses. We start with a general construction of covariant phase spaces admitting asymptotically conserved charges. The representation of the asymptotic symmetry algebra by a covariant Poisson bracket among the conserved charges is then defined and is shown to admit generically central extensions. The asymptotic structures of three three-dimensional spacetimes are then studied in detail and the consequences for quantum gravity in three dimensions are discussed.

Geoffrey Compčre

2007-08-23

269

Towards a quantum field theory of primitive string fields

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.

Ruehl, W., E-mail: wue_ruehl@t-online.de [Technical University of Kaiserslautern, Department of Physics (Germany)

2012-10-15

270

Towards a quantum field theory of primitive string fields

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 [2],[3]. 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 $AdS_{d+1}$ 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 $1\\leq N \\leq \\infty$ 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 $N=\\infty$. 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 $s \\geq 4$, they are distinguished by their anomalous dimensions (in $CFT_3$) or by their mass (in $AdS_4$). We sum over these multiplets and the spins to obtain "string type fields", one for each such monomial.

Werner Ruehl

2010-10-27

271

The Dual Description of Long Distance QCD and the Effective Lagrangian for Constituent Quarks

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.

Marshall Baker

1995-05-19

272

On open-closed extension of boundary string field theory

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.

Akira Ishida; Shunsuke Teraguchi

2012-07-11

273

Heterotic $?$'-corrections in Double Field Theory

We extend the generalized flux formulation of Double Field Theory to include all the first order bosonic contributions to the $\\alpha '$ expansion of the heterotic string low energy effective theory. The generalized tangent space and duality group are enhanced by $\\alpha'$ 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 $\\alpha'$ 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.

Oscar A. Bedoya; Diego Marques; Carmen Nunez

2014-07-01

274

Lattice field theory simulations of graphene

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.

Joaquín E. Drut; Timo A. Lähde

2009-01-06

275

Lattice field theory simulations of graphene

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.

Drut, Joaquín E

2009-01-01

276

Working Group Report: Lattice Field Theory

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.

Blum, T.; et al.,

2013-10-22

277

Even symplectic supermanifolds and double field theory

Over many decades, the word "double" has appeared in various contexts, at times seemingly unrelated. Several have some relation to mathematical physics. Recently, this has become particularly strking in DFT (double field theory). Two 'doubles' that are particularly relevant are double vector bundles and Drinfel'd doubles. The original Drinfel'd double occurred in the contexts of quantum groups and of Lie bialgebras. Quoting T. Voronov: "Double Lie algebroids arose in the works on double Lie groupoids and in connection with an analog for Lie bialgebroids of the classical Drinfel'd double of Lie bialgebras...Suppose $(A,A^*)$ is a Lie bialgebroid over a base $M$... Mackenzie and Roytenberg suggested two different constructions based on the cotangent bundles $T^*A$ and $T^*\\Pi A$, respectively. Here $\\Pi$ is the fibre-wise parity reversal functor." Although the approaches of Roytenberg and of Mackenzie look very different, Voronov establishes their equivalence. We have found Roytenberg's version to be quite congenial with our attempt to interpret the gauge algebra of DFT in terms of Poisson brackets on a suitable generalized Drinfel'd double. This double of a Lie bialgebroid $(A,A^*)$ provides a framework to describe the differentials of $A$ and $A^*$ on an equal footing as Hamiltonian functions on an even symplectic supermanifold. A special choice of momenta explicates the double coordinates of DFT and shows their relation to the strong constraint determining the physical fields of double field theory.

Andreas Deser; Jim Stasheff

2014-06-13

278

The effective field theory of dark energy

We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar can always be de-mixed from gravity at quadratic order in the perturbations, but not necessarily through a conformal rescaling of the metric. We show how to express covariant field-operators in our formalism and give several explicit examples of dark energy and modified gravity models in our language. Finally, we discuss the relation with the covariant EFT methods recently appeared in the literature.

Gubitosi, Giulia; Vernizzi, Filippo [CEA, IPhT, 91191 Gif-sur-Yvette cédex (France); Piazza, Federico, E-mail: giulia.gubitosi@roma1.infn.it, E-mail: fpiazza@apc.univ-paris7.fr, E-mail: filippo.vernizzi@cea.fr [Paris Center for Cosmological Physics (PCCP) and Laboratoire APC, Université Paris 7, 75205 Paris (France)

2013-02-01

279

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

280

Microscopic Fields and Macroscopic Averages in Einstein's Unified Field Theory

The relation between microscopic and macroscopic entities in the generally covariant theories is considered, and it is argued that a sensible definition of the macroscopic averages requires a restriction of the allowed transformations of coordinates. Spacetime averages of the geometric objects of Einstein's unified field theory are then defined, and the reconstruction of some features of macroscopic reality from hypothetic microscopic structures is attempted. It is shown how a fluctuating microscopic behaviour of the metric field can rule the constitutive relation for electromagnetism both in vacuo and in nondispersive material media. Moreover, if both the metric and the skew tensor density that represents the electric displacement and the magnetic field are assumed to possess a wavy microscopic structure, nonvanishing generalized force densities can appear in the continuum. They originate from a resonance process, in which at least three waves need to be involved. This process only occurs if the wavevectors fulfil the three-wave resonance condition, so ubiquitous in quantum physics. The wavy behaviour of the metric is essential for the occurrence of this resonance phenomenon.

S. Antoci

1998-01-15

281

A Survey of Lagrangian Mechanics and Control on Lie algebroids and groupoids

In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical control systems, Discrete Mechanics and extensions to Classical Field Theory within a single framework. Various examples along the discussion illustrate the soundness of the approach.

Jorge Cortes; Manuel de Leon; Juan C. Marrero; D. Martin de Diego; Eduardo Martinez

2005-11-03

282

He??6 in cluster effective field theory

NASA Astrophysics Data System (ADS)

The hypernucleus He??6 is studied as a three-body (???) cluster system in cluster effective field theory at leading order. We find that the three-body contact interaction exhibits the limit cycle when the cutoff in the integral equations is sent to the asymptotic limit and thus it should be promoted to leading order. We also derive a determination equation of the limit cycle which reproduces the numerically obtained limit cycle. We then study the correlations between the double ? separation energy B?? of He??6 and the scattering length a?? of the S-wave ?? scattering. The role of the scale in this approach is also discussed.

Ando, Shung-Ichi; Oh, Yongseok

2014-09-01

283

Purely cubic action for string field theory

NASA Technical Reports Server (NTRS)

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.

Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.

1986-01-01

284

Stochastic inflation and replica field theory

NASA Astrophysics Data System (ADS)

We adopt methods from statistical field theory to stochastic inflation. For the example of a free test field in de Sitter and power-law inflation, the power spectrum of long-wavelength fluctuations is computed. We study its dependence on the shape of the filter that separates long- from short-wavelength modes. While for filters with infinite support the phenomenon of dimensional reductions is found on large superhorizon scales, filters with compact support return a scale-invariant power spectrum in the infrared. Features of the power spectrum, induced by the filter, decay within a few e-foldings. Thus the late-time power spectrum is independent of the filter details.

Kühnel, Florian; Schwarz, Dominik J.

2009-02-01

285

Bekenstein bound in asymptotically free field theory

For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality (S/E){<=}2{pi}R, where R stands for the radius of the smallest sphere that circumscribes the system. The validity of the Bekenstein bound in the asymptotically free side of the Euclidean ({lambda}{phi}{sup 4}){sub d} scalar field theory is investigated. We consider the system in thermal equilibrium with a reservoir at temperature {beta}{sup -1} and defined in a compact spatial region without boundaries. Using the effective potential, we discuss the thermodynamic of the model. For low and high temperatures the system presents a condensate. We present the renormalized mean energy E and entropy S for the system and show in which situations the specific entropy satisfies the quantum bound.

Arias, E.; Svaiter, N. F.; Menezes, G. [Centro Brasileiro de Pesquisas Fisicas-CBPF, Rua Dr. Xavier Sigaud 150, Rio de Janeiro, RJ, 22290-180 (Brazil); Instituto de Fisica Teorica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, Sao Paulo, SP, 01140-070 (Brazil)

2010-08-15

286

Bondi mass in classical field theory

We analyze three classical field theories based on the wave equation: scalar field, electrodynamics and linearized gravity. We derive certain generating formula on a hyperboloid and on a null surface for them. The linearized Einstein equations are analyzed around null infinity. It is shown how the dynamics can be reduced to gauge invariant quanitities in a quasi-local way. The quasi-local gauge-invariant ``density'' of the hamiltonian is derived on the hyperboloid and on the future null infinity. The result gives a new interpretation of the Bondi mass loss formula. We show also how to define angular momentum. Starting from affine approach for Einstein equations we obtain variational formulae for Bondi-Sachs type metrics related with energy and angular momentum generators. The original van der Burg asymptotic hierarchy is revisited and the relations between linearized and asymptotic nonlinear situations are established. We discuss also supertranslations, Newman-Penrose charges and Janis solutions.

Jacek Jezierski

1997-03-27

287

PT-Symmetric Quantum Field Theory

In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H{sup {dagger}}) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.

Bender, Carl M. [Physics Department, Washington University, St. Louis, MO 63130 (United States)

2011-09-22

288

A conformal field theory for eternal inflation?

NASA Astrophysics Data System (ADS)

We study a statistical model defined by a conformally invariant distribution of overlapping spheres in arbitrary dimension d. The model arises as the asymptotic distribution of cosmic bubbles in d+1 dimensional de Sitter space, and also as the asymptotic distribution of bubble collisions with the domain wall of a fiducial ``observation bubble'' in d+2 dimensional de Sitter space. In this note we calculate the 2-, 3-, and 4-point correlation functions of exponentials of the ``bubble number operator'' analytically in d = 2. We find that these correlators are free of infrared divergences, covariant under the global conformal group, charge conserving, and transform with positive conformal dimensions that are related in a novel way to the charge. Although by themselves these operators probably do not define a full-fledged conformal field theory, one can use the partition function on a sphere to compute an approximate central charge in the 2D case. The theory in any dimension has a noninteracting limit when the nucleation rate of the bubbles in the bulk is very large. The theory in two dimensions is related to some models of continuum percolation, but it is conformal for all values of the tunneling rate.

Freivogel, Ben; Kleban, Matthew

2009-12-01

289

NASA Astrophysics Data System (ADS)

General Relativity is the standard framework by which all gravitational systems are analyzed in modern research, and it provides the theme for all the investigations in this thesis. Beyond this common platform, very different gravitating problems are examined here, and several analytical approaches are used to investigate these systems. Effective field theory, a methodological approach prominent in quantum field theory, plays an important role in the analysis of two of the problems in this thesis. In the first instance, an effective field theory for bound gravitational states is used to compute the interaction Lagrangian of a binary system at the second post-Newtonian order. A metric parametrization based on a temporal Kaluza-Klein decomposition is also used. In this effective field theory calculation, the post-Newtonian results for the equations of motion are elegantly reproduced. In the next problem considered, effective field theory is used to investigate the thermodynamics of compactified charged black holes. The relevant thermodynamic quantities are all computed to second order in the perturbation parameter and finite size effects are incorporated through higher order worldline operators. Complete agreement is found with an exact extremal black hole solution constructed with traditional General Relativistic methods. The results indicate that the addition of charge to a compactified black hole may delay the phase transition to a black string. Finally, the third problem examined here concerns the evolution of perturbations at the end of early universe inflation. General Relativity enters this problem through cosmological perturbation theory. It is shown that the coherent oscillations in the inflaton break down at the comoving post-inflationary horizon size, about 14 e-folds after the end of inflation. This is many e-folds before any known constraints, leading to possible implications for the matching problem of inflation, and the generation of stochastic gravitational waves in the post-inflationary universe.

Gilmore, James Brian

2010-12-01

290

Perfect magnetohydrodynamics as a field theory

We propose the generally covariant action for the theory of a self-coupled complex scalar field and electromagnetism which by virtue of constraints is equivalent, in the regime of long wavelengths, to perfect magnetohydrodynamics (MHD). We recover from it the Euler equation with Lorentz force, and the thermodynamic relations for a prefect fluid. The equation of state of the latter is related to the scalar field's self potential. We introduce 1+3 notation to elucidate the relation between MHD and field variables. In our approach the requirement that the scalar field be single valued leads to the quantization of a certain circulation in steps of ({Dirac_h}/2{pi}); this feature leads, in the classical limit, to the conservation of that circulation. The circulation is identical to that in Oron's generalization of Kelvin's circulation theorem to perfect MHD; we here characterize the new conserved helicity associated with it. We also demonstrate the existence for MHD of two Bernoulli-like theorems for each spacetime symmetry of the flow and geometry; one of these is pertinent to suitably defined potential flow. We exhibit the conserved quantities explicitly in the case that two symmetries are simultaneously present, and give examples. Also in this case we exhibit a new conserved MHD circulation distinct from Oron's, and provide an example.

Bekenstein, Jacob D.; Betschart, Gerold [Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel)

2006-10-15

291

Refringence, field theory, and normal modes

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.

C. Barcelo; S. Liberati; Matt Visser

2001-11-19

292

Supersymmetric Field Theory Based on Generalized Uncertainty Principle

We construct a quantum theory of free fermion field based on the generalized uncertainty principle using supersymmetry as a guiding principle. A supersymmetric field theory with a real scalar field and a Majorana fermion field is given explicitly and we also find that the supersymmetry algebra is deformed from an usual one.

Yuuichirou Shibusa

2007-04-12

293

Quantum field theory methods and inflationary universe models

This paper reviews the theory of inflationary universe models, giving particular emphasis to the question of origin and growth of energy-density fluctuations in these new cosmologies. The first four sections constitute a pedagogical introduction to some of the important quantum field theory methods used in inflationary universe scenarios: calculation of the effective potential, finite-temperature quantum field theory, analysis of the decay of a metastable quantum state, and free field theory in curved space-time.

Brandenberger, R.H.

1985-01-01

294

Topics in field theories in lower dimensions

NASA Astrophysics Data System (ADS)

In this thesis, we discuss three problems in gauge theory. First, we discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of an abelian magnetic monopole and note that the Hamiltonian is not self- adjoint in the lowest two angular momentum modes. We then use von Neumann's theory of self-adjoint extensions to construct a self-adjoint operator with the same functional form. In general, this operator will have eigenstates in which the lowest two angular momentum modes mix, thereby removing conservation of angular momentum. However, consistency with the Dirac equation limits the possibilities such that conservation of angular momentum is in fact not lost. Because the same effect occurs for a spinless particle with a sufficiently attractive inverse square potential, we also study this system. We use this simpler Hamiltonian to compare the eigenfunctions corresponding to a particular self-adjoint extension with the eigen-functions satisfying a boundary condition consistent with probability conservation. Second, we examine a system with charged vector mesons interacting with a constant external magnetic field in 2 + 1 dimensions. We look at the eigenvalue problem of the operator corresponding to the equations of motion, and use these solutions to obtain the propagator. Third, we consider a charged scalar field propagating in a constant external electric field in 1 + 1 dimensions. The interesting property of this simple system is that it has a central charge in its classical Poincaré algebra. In order to check Poincaré invariance, we modify the energy-momentum tensor such that it satisfies the Dirac-Schwinger relation. Next, we quantize the system and show that the massless case is exactly solvable. Finally, we show that the algebra after quantization holds without anomalies.

Karat, Edwin Richard

295

Local superfield Lagrangian BRST quantization

NASA Astrophysics Data System (ADS)

A ?-local formulation of superfield Lagrangian quantization in non-Abelian hypergauges is proposed on the basis of an extension of general reducible gauge theories to special superfield models with a Grassmann parameter ?. We solve the problem of describing the quantum action and the gauge algebra of an L-stage-reducible superfield model in terms of a BRST charge for a formal dynamical system with first-class constraints of (L+1)-stage reducibility. Starting from ?-local functions of the quantum and gauge-fixing actions, with an essential use of Darboux coordinates on the antisymplectic manifold, we construct a superfield generating functionals of Green's functions, including the effective action. We present two superfield forms of BRST transformations, considered as ?-shifts along vector fields defined by Hamiltonian-like systems constructed in terms of the quantum and gauge-fixing actions and an arbitrary ?-local boson function, as well as in terms of corresponding fermion functionals, through Poisson brackets with opposite Grassmann parities. The gauge independence of the S-matrix is proved. The Ward identities are derived. Connection is established with the BV method, the multilevel Batalin-Tyutin formalism, as well as with the superfield quantization scheme of Lavrov, Moshin, and Reshetnyak, extended to the case of general coordinates.

Gitman, D. M.; Moshin, P. Yu.; Reshetnyak, A. A.

2005-07-01

296

Symmetries and defects in three-dimensional topological field theory

Boundary conditions and defects of any codimension are natural parts of any quantum field theory. Surface defects in three-dimensional topological field theories of Turaev-Reshetikhin type have applications to two-dimensional conformal field theories, in solid state physics and in quantum computing. We explain an obstruction to the existence of surface defects that takes values in a Witt group. We then turn to surface defects in Dijkgraaf-Witten theories and their construction in terms of relative bundles; this allows one to exhibit Brauer-Picard groups as symmetry groups of three-dimensional topological field theories.

Jurgen Fuchs; Christoph Schweigert

2015-01-08

297

Symmetries and defects in three-dimensional topological field theory

Boundary conditions and defects of any codimension are natural parts of any quantum field theory. Surface defects in three-dimensional topological field theories of Turaev-Reshetikhin type have applications to two-dimensional conformal field theories, in solid state physics and in quantum computing. We explain an obstruction to the existence of surface defects that takes values in a Witt group. We then turn to surface defects in Dijkgraaf-Witten theories and their construction in terms of relative bundles; this allows one to exhibit Brauer-Picard groups as symmetry groups of three-dimensional topological field theories.

Fuchs, Jurgen

2015-01-01

298

A unified field theory of mesons and baryons

The way in which a nonlinear meson type of field theory may contain its ; own sources, and how these may be idealized to point singularities as in the ; conventional field theories of interacting linear systems, is formulated. The ; structure of the particle source in the classical theory is caleulated, and some ; qualitative features of the interactions

T. Skyrme; T. H. R

1962-01-01

299

Quantum field theory methods and inflationary universe models

This paper reviews the theory of inflationary universe models, giving particular emphasis to the question of origin and growth of energy-density fluctuations in these new cosmologies. The first four sections constitute a pedagogical introduction to some of the important quantum field theory methods used in inflationary universe scenarios: calculation of the effective potential, finite-temperature quantum field theory, analysis of the

Robert Brandenberger

1985-01-01

300

String Calculus: Conformal Field Theory as a Tool in String Theory

String Calculus: Conformal Field Theory as a Tool in String Theory Emil Martinec Enrico Fermi Inst, in the guise of string theory. String theory promises an elegant synthesis of quan- tum mechanics (algebra in string theory in the description of perturbative string propagation. However, one might believe

Gardel, Margaret

301

Matrix Product States for Gauge Field Theories

NASA Astrophysics Data System (ADS)

The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.

Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank

2014-08-01

302

Matrix product states for gauge field theories.

The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field. PMID:25215973

Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank

2014-08-29

303

Triton Photodisintegration with Effective Field Theory

Effective field theory (EFT) has been recently used for the calculation of neutron-deuteron radiative capture at very low energies.We present here the use of EFT to calculate the two-body photodisintegration of the triton, considering the three-body force. The calculated cross section shows sharp rising from threshold to maximum about 0.88 mb at 13 MeV and decreasing slightly to about 0.81 mb at 19 MeV, in agreement with the experimental data. Our results are in good agreement with the experimental data and the other calculations using modern realistic two- and three-nucleon forces, like AV18/UrbanaIX potential.

H. Sadeghi; S. Bayegan

2009-08-16

304

Quantum field theory and time machines

We analyze the "F-locality condition" (proposed by Kay to be a mathematical implementation of a philosophical bias related to the equivalence principle, we call it the "GH-equivalence principle"), which is often used to build a generalization of quantum field theory to non-globally hyperbolic spacetimes. In particular we argue that the theorem proved by Kay, Radzikowski, and Wald to the effect that time machines with compactly generated Cauchy horizons are incompatible with the F-locality condition actually does not support the "chronology protection conjecture", but rather testifies that the F-locality condition must be modified or abandoned. We also show that this condition imposes a severe restriction on the geometry of the world (it is just this restriction that comes into conflict with the existence of a time machine), which does not follow from the above mentioned philosophical bias. So, one need not sacrifice the GH-equivalence principle to "emend" the F-locality condition. As an example we consider a particular modification, the "MF-locality condition". The theory obtained by replacing the F-locality condition with the MF-locality condition possesses a few attractive features. One of them is that it is consistent with both locality and the existence of time machines.

S. Krasnikov

1998-10-13

305

Multidimensional wave field signal theory: Mathematical foundations

NASA Astrophysics Data System (ADS)

Many important physical phenomena are described by wave or diffusion-wave type equations. Since these equations are linear, it would be useful to be able to use tools from the theory of linear signals and systems in solving related forward or inverse problems. In particular, the transform domain signal description from linear system theory has shown concrete promise for the solution of problems that are governed by a multidimensional wave field. The aim is to develop a unified framework for the description of wavefields via multidimensional signals. However, certain preliminary mathematical results are crucial for the development of this framework. This first paper on this topic thus introduces the mathematical foundations and proves some important mathematical results. The foundation of the framework starts with the inhomogeneous Helmholtz or pseudo-Helmholtz equation, which is the mathematical basis of a large class of wavefields. Application of the appropriate multi-dimensional Fourier transform leads to a transfer function description. To return to the physical spatial domain, certain mathematical results are necessary and these are presented and proved here as six fundamental theorems. These theorems are crucial for the evaluation of a certain class of improper integrals which arise in the evaluation of inverse multi-dimensional Fourier and Hankel transforms, upon which the framework is based. Subsequently, applications of these theorems are demonstrated, in particular for the derivation of Green's functions in different coordinate systems.

Baddour, Natalie

2011-06-01

306

Quantum spectral dimension in quantum field theory

We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory, when the system is probed at a given resolution. This picture has three main advantages: (a) it clarifies the role of the mass term in the derivation of the spectral dimension; (b) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where instead of a transition amplitude one has a probability density solving a non-relativistic diffusion equation in an abstract diffusion time; (c) it solves the problem of negative probabilities known for higher-order and non-local dispersion relations in classical and quantum gravity; (d) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension $d_s$ of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension $D$. In particular, in the presence of higher momentum powers it changes with the scale, dropping from $D$ in the infrared (IR) to a value $d_s^{\\rm UV}\\leq D$ in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value $d_s^{\\rm UV}=2$ for any dimension $D$.

Gianluca Calcagni; Leonardo Modesto; Giuseppe Nardelli

2014-08-01

307

Mean field theory of charged dendrimer molecules.

Using self-consistent field theory (SCFT), we study the conformational properties of polyelectrolyte dendrimers. We compare results for three different models of charge distributions on the polyelectrolytes: (1) a smeared, quenched charge distribution characteristic of strong polyelectrolytes; (2) a smeared, annealed charge distribution characteristic of weak polyelectrolytes; and (3) an implicit counterion model with Debye-Huckel interactions between the charged groups. Our results indicate that an explicit treatment of counterions is crucial for the accurate characterization of the conformations of polyelectrolyte dendrimers. In comparing the quenched and annealed models of charge distributions, annealed dendrimers were observed to modulate their charges in response to the density of polymer monomers, counterions, and salt ions. Such phenomena is not accommodated within the quenched model of dendrimers and is shown to lead to significant differences between the predictions of quenched and annealed model of dendrimers. In this regard, our results indicate that the average dissociated charge ? inside the dendrimer serves as a useful parameter to map the effects of different parametric conditions and models onto each other. We also present comparisons to the scaling results proposed to explain the behavior of polyelectrolyte dendrimers. Inspired by the trends indicated by our results, we develop a strong segregation theory model whose predictions are shown to be in very good agreement with the numerical SCFT calculations. PMID:22128954

Lewis, Thomas; Pryamitsyn, Victor; Ganesan, Venkat

2011-11-28

308

Hamiltonian constraint in polymer parametrized field theory

Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.

Laddha, Alok [Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, Pennsylvania 16802-6300 (United States); Chennai Mathematical Institute, SIPCOT IT Park, Padur PO, Siruseri 603103 (India); Raman Research Institute, Bangalore-560 080 (India); Varadarajan, Madhavan [Raman Research Institute, Bangalore-560 080 (India)

2011-01-15

309

An assessment of Evans' unified field theory II

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for Evans' theory and show that it yields two field equations. The second field equation is algebraic in the torsion and we can resolve it with respect to the torsion. It turns out that for all physical cases the torsion vanishes and the first field equation, together with Evans' unified field theory, collapses to an ordinary Einstein equation.

Friedrich W. Hehl; Yuri N. Obukhov

2007-03-10

310

Topological field theory of dynamical systems.

Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the "edge of chaos." Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed. PMID:23020473

Ovchinnikov, Igor V

2012-09-01

311

Topological field theory of dynamical systems

Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the 'edge of chaos.' Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.

Ovchinnikov, Igor V. [Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, California 90095-1594 (United States)

2012-09-15

312

Topological field theory of dynamical systems

NASA Astrophysics Data System (ADS)

Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the "edge of chaos." Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.

Ovchinnikov, Igor V.

2012-09-01

313

The IR-resummed Effective Field Theory of Large Scale Structures

NASA Astrophysics Data System (ADS)

We present a new method to resum the effect of large scale motions in the Effective Field Theory of Large Scale Structures. Because the linear power spectrum in ?CDM is not scale free the effects of the large scale flows are enhanced. Although previous EFT calculations of the equal-time density power spectrum at one and two loops showed a remarkable agreement with numerical results, they also showed a 2% residual which appeared related to the BAO oscillations. We show that this was indeed the case, explain the physical origin and show how a Lagrangian based calculation removes this differences. We propose a simple method to upgrade existing Eulerian calculations to effectively make them Lagrangian and compare the new results with existing fits to numerical simulations. Our new two-loop results agrees with numerical results up to k~ 0.6 h Mpc?1 to within 1% with no oscillatory residuals. We also compute power spectra involving momentum which is significantly more affected by the large scale flows. We show how keeping track of these velocities significantly enhances the UV reach of the momentum power spectrum in addition to removing the BAO related residuals. We compute predictions for the real space correlation function around the BAO scale and investigate its sensitivity to the EFT parameters and the details of the resummation technique.

Senatore, Leonardo; Zaldarriaga, Matias

2015-02-01

314

Twist Field as Three String Interaction Vertex in Light Cone String Field Theory

It has been suggested that matrix string theory and light-cone string field theory are closely related. In this paper, we investigate the relation between the twist field, which represents string interactions in matrix string theory, and the three-string interaction vertex in light-cone string field theory carefully. We find that the three-string interaction vertex can reproduce some of the most important OPEs satisfied by the twist field.

Isao Kishimoto; Sanefumi Moriyama; Shunsuke Teraguchi

2007-03-22

315

Symplectic rigidity: Lagrangian submanifolds

\\u000a This chapter is supposed to be a summary of what is known today about Lagrangian embeddings. We emphasise the difference between\\u000a flexibility results, such as the h-principle of Gromov applied here to Lagrangian immersions (and also to the construction of examples of Lagrangian embeddings)\\u000a and rigidity theorems, based on existence theorems for pseudo-holomorphic curves.

Michčle Audin; François Lalonde; Leonid Polterovich

316

Seeking the balance: Patching double and exceptional field theories

We investigate the patching of double and exceptional field theories. In double field theory the patching conditions imposed on the spacetime after solving the strong section condition imply that the 3-form field strength $H$ is exact. A similar conclusion can be reached for the form field strengths of exceptional field theories after some plausive assumptions are made on the relation between the transition functions of the additional coordinates and the patching data of the form field strengths. We illustrate the issues that arise, and explore several alternative options which include the introduction of C-folds and of the topological geometrisation condition.

G. Papadopoulos

2014-02-11

317

Quantum Open-Closed Homotopy Algebra and String Field Theory

We reformulate the algebraic structure of Zwiebach's quantum open-closed string field theory in terms of homotopy algebras. We call it the quantum open-closed homotopy algebra (QOCHA) which is the generalization of the open-closed homotopy algebra (OCHA) of Kajiura and Stasheff. The homotopy formulation reveals new insights about deformations of open string field theory by closed string backgrounds. In particular, deformations by Maurer Cartan elements of the quantum closed homotopy algebra define consistent quantum open string field theories.

Korbinian Muenster; Ivo Sachs

2011-10-19

318

Reggeon Field Theory for Large Pomeron Loops

We analyze the range of applicability of the high energy Reggeon Field Theory $H_{RFT}$ derived in [1]. We show that this theory is valid as long as at any intermediate value of rapidity $\\eta$ throughout the evolution at least one of the colliding objects is dilute. Importantly, at some values of $\\eta$ the dilute object could be the projectile, while at others it could be the target, so that $H_{RFT}$ does not reduce to either $H_{JIMWLK}$ or $H_{KLWMIJ}$. When both objects are dense, corrections to the evolution not accounted for in [1] become important. The same limitation applies to other approaches to high energy evolution available today, such as for example [3] and [4]. We also show that, in its regime of applicability $H_{RFT}$ can be simplified. We derive the simpler version of $H_{RFT}$ and in the large $N_c$ limit rewrite it in terms of the Reggeon creation and annihilation operators. The resulting $H_{RFT}$ is explicitly self dual and provides the generalization of the Pomeron calculus developed in [4] by including higher Reggeons in the evolution. It is applicable for description of `large' Pomeron loops, namely Reggeon graphs where all the splittings occur close in rapidity to one dilute object (projectile), while all the merging close to the other one (target). Additionally we derive, in the same regime expressions for single and double inclusive gluon production (where the gluons are not separated by a large rapidity interval) in terms of the Reggeon degrees of freedom.

Tolga Altinoluk; Alex Kovner; Eugene Levin; Michael Lublinsky

2014-01-29

319

On the conformal field theory of the Higgs branch

We study 1+1-dimensional theories of vector and hypermultiplets with (4,4) supersymmetry. Despite strong infrared fluctuations, these theories flow in general to distinct conformal field theories on the Coulomb and Higgs branches. In some cases there may be a quantum Higgs theory even when there is no classical Higgs branch. The Higgs branches of certain such theories provide a framework for

Edward Witten

1997-01-01

320

Halo nuclei interactions using effective field theory

NASA Astrophysics Data System (ADS)

Effective field theory (EFT) provides a framework to exploit separation of scales in the physical system in order to perform systematic model-independent calculations. There has been significant interest in applying the methods of EFT to halo nuclei. Using halo effective field theory, I provide a model-independent calculation of the radiative neutron capture on lithium-7 over an energy range where the contribution from the 3+ resonance becomes important. This reaction initiate the sequence in the carbon-nitrogen-oxygen (CNO) cycle in the inhomogeneous BBN models, and determine the amount of heavy element production from its reaction rate. One finds that a satisfactory description of the capture reaction, in the present single-particle approximation, suggests the use of a resonance width about three times larger than the experimental value. Power counting arguments that establish a hierarchy for the electromagnetic one- and two-body currents is also presented. The neutron capture of Lithium7 calculation has direct impact on the proton capture on beryllium7 which plays an important role in the neutrino experiments studying physics beyond the Standard Model of particle physics. As a further study of halo nuclei interactions, the cross section of radiative capture of a neutron by carbon-14 is calculated by considering the dominant contribution from electric dipole transition. This is also a part of the CNO cycle and as the slowest reaction in the chain it limits the flow of the production of heavier nuclei A > 14. The cross section is expressed in terms of the elastic scattering parameters of an effective range expansion. Contributions from both the resonant and non-resonant interactions are calculated. Significant interferences between these leads to a capture contribution that deviates from a simple Breit-Wigner resonance form. Using EFT, I present electromagnetic form factors of several halo nuclei. The magnetic dipole moment and the charge radii of carbon-15, beryllium-11, and carbon-19 halo systems are considered. Prediction is made for the magnetic moment in the leading order. I can only provide some estimates for the form factors in next-to-leading order where two-body currents appear. The estimates are based on power counting unless the effective range and the magnetic moment are known. Charge radii for three systems have also been estimated at LO and NLO.

Fernando, Nippalage Lakma Kaushalya

321

Short-range interactions in an effective field theory approach for nucleon-nucleon scattering

We investigate in detail the effect of making the range of the ``contact'' interaction used in effective field theory (EFT) calculations of NN scattering finite. This is done in both an effective field theory with explicit pions, and one where the pions have been integrated out. In both cases we calculate NN scattering in the ${}^1 S_0$ channel using potentials which are second-order in the EFT expansion. The contact interactions present in the EFT Lagrangian are made finite by use of a square-well regulator. We find that there is an optimal radius for this regulator, at which second-order corrections to the EFT are identically zero; for radii near optimal these second-order corrections are small. The cutoff EFTs which result from this procedure appear to be valid for momenta up to about 100 MeV/c. We also find that the radius of the square well cannot be reduced to zero if the theory is to reproduce both the experimental scattering length and effective range. Indeed, we show that, if the NN potential is the ...

Scaldeferri, K A; Kao, C W; Cohen, T D

1996-01-01

322

Effective field theories for rooted staggered fermions

We extend the construction of the Symanzik effective action to include rooted staggered fermions, starting from a generalization of the renormalization-group approach to rooted staggered fermions. The Symanzik action, together with the usual construction of a partially quenched chiral effective theory from a local, partially quenched, fundamental theory, can then be used to derive the chiral effective theory. The latter reproduces rooted staggered chiral perturbation theory.

Claude Bernard; Maarten Golterman; Yigal Shamir

2007-09-13

323

Gravitational consequences of modern field theories

NASA Technical Reports Server (NTRS)

Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.

Horowitz, Gary T.

1989-01-01

324

Gravitational Descendants in Symplectic Field Theory

NASA Astrophysics Data System (ADS)

It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown using the ideas in Okounkov and Pandharipande (Ann Math 163(2):517-560, 2006) that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits, the gravitational descendants have a geometric interpretation in terms of branching conditions, we follow the ideas in Cieliebak and Latschev (

Fabert, Oliver

2011-02-01

325

This paper attempts to analyze central place theory of spatial economics based on supply and demand theory in microeconomics and field theory in physics, and also discuss their relationship. Three most important research findings are described below. Firstly, the concept of market equilibrium could be expressed in the mathematical form of physics field theory under proper hypothesis. That is because the most important aspect of field theory model is that complex analysis is taken as a key mathematical tool. If assuming that imaginary part is neglected in this model, it is found that this model has the same mathematical structure as supply and demand theory of microeconomics. Secondly, the mathematical model of field theory can be applied to express clearly many concepts of central place theory, or even introduce many new concepts. Thirdly, it could also be taken as a study of combining the Hotelling Model and Moses Model for the location theory in another mathematic approach.

Benjamin Chih-Chien Nien

2006-10-11

326

The gauge algebra of double field theory and Courant brackets

We investigate the symmetry algebra of the recently proposed field theory on a doubled torus that describes closed string modes on a torus with both momentum and winding. The gauge parameters are constrained fields on the ...

Hull, Chris

327

Lagrangian for the Frenkel electron

NASA Astrophysics Data System (ADS)

We found Lagrangian action which describes spinning particle on the base of non-Grassmann vector and involves only one auxiliary variable. It provides the right number of physical degrees of freedom and yields generalization of the Frenkel and BMT equations to the case of an arbitrary electromagnetic field. For a particle with anomalous magnetic moment, singularity in the relativistic equations generally occurs at the speed different from the speed of light.

Deriglazov, Alexei A.

2014-09-01

328

Field theory on R× S 3 topology. VI: Gravitation

NASA Astrophysics Data System (ADS)

We extend to curved space-time the field theory on R×S3 topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU2 gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.

Carmeli, M.; Malin, S.

1987-04-01

329

Effective Lagrangians for quantum many-body systems

The low-energy and low-momentum dynamics of systems with a spontaneously broken continuous symmetry is dominated by the ensuing Nambu-Goldstone bosons. It can be conveniently encoded in a model-independent effective field theory whose structure is fixed by symmetry up to a set of effective coupling constants. We construct the most general effective Lagrangian for the Nambu-Goldstone bosons of spontaneously broken global internal symmetry up to the fourth order in derivatives. Rotational invariance and spatial dimensionality of one, two or three are assumed in order to obtain compact explicit expressions, but our method is completely general and can be applied without modifications to condensed matter systems with a discrete space group as well as to higher-dimensional theories. The general low-energy effective Lagrangian for relativistic systems follows as a special case. We also discuss the effects of explicit symmetry breaking and classify the corresponding terms in the Lagrangian. Diverse examples are worked out in order to make the results accessible to a wide theoretical physics community.

Jens O. Andersen; Tomas Brauner; Christoph P. Hofmann; Aleksi Vuorinen

2014-06-13

330

Effective Lagrangians for quantum many-body systems

NASA Astrophysics Data System (ADS)

The low-energy and low-momentum dynamics of systems with a spontaneously broken continuous symmetry is dominated by the ensuing Nambu-Goldstone bosons. It can be conveniently encoded in a model-independent effective field theory whose structure is fixed by symmetry up to a set of effective coupling constants. We construct the most general effective Lagrangian for the Nambu-Goldstone bosons of spontaneously broken global internal symmetry up to fourth order in derivatives. Rotational invariance and spatial dimensionality of one, two or three are assumed in order to obtain compact explicit expressions, but our method is completely general and can be applied without modifications to condensed matter systems with a discrete space group as well as to higher-dimensional theories. The general low-energy effective Lagrangian for relativistic systems follows as a special case. We also discuss the effects of explicit symmetry breaking and classify the corresponding terms in the Lagrangian. Diverse examples are worked out in order to make the results accessible to a wide theoretical physics community.

Andersen, Jens O.; Brauner, Tomá; Hofmann, Christoph P.; Vuorinen, Aleksi

2014-08-01

331

Effective field theory of slowly moving `extreme black holes'

NASA Astrophysics Data System (ADS)

We consider the non-relativistic effective field theory of `extreme black holes' in the Einstein-Maxwell-dilaton theory with an arbitrary dilaton coupling. We investigate the finite-temperature behaviour of a gas of `extreme black holes' using the effective theory. The total energy of the classical many-body system is also derived.

Degura, Yoshitaka; Shiraishi, Kiyoshi

2000-10-01

332

Lattice p-Form Electromagnetism and Chain Field Theory

Since Wilson's work on lattice gauge theory in the 1970s, discrete versions of field theories have played a vital role in fundamental physics. But there is recent interest in certain higher dimensional analogues of gauge theory, such as p-form electromagnetism, including the Kalb-Ramond field in string theory, and its nonabelian generalizations. It is desirable to discretize such `higher gauge theories' in a way analogous to lattice gauge theory, but with the fundamental geometric structures in the discretization boosted in dimension. As a step toward studying discrete versions of more general higher gauge theories, we consider the case of p-form electromagnetism. We show that discrete p-form electromagnetism admits a simple algebraic description in terms of chain complexes of abelian groups. Moreover, the model allows discrete spacetimes with quite general geometry, in contrast to the regular cubical lattices usually associated with lattice gauge theory. After constructing a suitable model of discrete spacetime for p-form electromagnetism, we quantize the theory using the Euclidean path integral formalism. The main result is a description of p-form electromagnetism as a `chain field theory' -- a theory analogous to topological quantum field theory, but with chain complexes replacing manifolds. This, in particular, gives a notion of time evolution from one `spacelike slice' of discrete spacetime to another.

Derek K. Wise

2005-10-08

333

Extended gyrokinetic field theory for time-dependent magnetic confinement fields

A gyrokinetic system of equations for turbulent toroidal plasmas in time-dependent axisymmetric background magnetic fields is derived from the variational principle. Besides governing equations for gyrocenter distribution functions and turbulent electromagnetic fields, the conditions which self-consistently determine the background magnetic fields varying on a transport time scale are obtained by using the Lagrangian, which includes the constraint on the background fields. Conservation laws for energy and toroidal angular momentum of the whole system in the time-dependent background magnetic fields are naturally derived by applying Noether's theorem. It is shown that the ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work agree with the results from the conventional recursive formulation with the WKB representation except that collisional effects are disregarded here.

Sugama, H.; Watanabe, T.-H.; Nunami, M. [National Institute for Fusion Science, Toki 509-5292 (Japan)] [National Institute for Fusion Science, Toki 509-5292 (Japan)

2014-01-15

334

Accelerating Universes in String Theory via Field Redefinition

We study cosmological solutions in the effective heterotic string theory with $\\alpha'$-correction terms in string frame. It is pointed out that the effective theory has an ambiguity via field redefinition and we analyze generalized effective theories due to this ambiguity. We restrict our analysis to the effective theories which give equations of motion of second order in the derivatives, just as "Galileon" field theory. This class of effective actions contains two free coupling constants. We find de Sitter solutions as well as the power-law expanding universes in our four-dimensional Einstein frame. The accelerated expanding universes are always the attractors in the present dynamical system.

Kei-ichi Maeda; Nobuyoshi Ohta; Ryo Wakebe

2014-06-09

335

Dynamics of polymers: A mean-field theory

We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose (MSR) type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field ? and a conjugate MSR response field ?, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamics involving hybrid particle-field simulation techniques such as the single-chain in mean-field method.

Fredrickson, Glenn H. [Department of Chemical Engineering, University of California, Santa Barbara, California 93106 (United States) [Department of Chemical Engineering, University of California, Santa Barbara, California 93106 (United States); Materials Research Laboratory, University of California, Santa Barbara, California 93106 (United States); Department of Materials, University of California, Santa Barbara, California 93106 (United States); Orland, Henri [Institut de Physique Théorique, CE-Saclay, CEA, F-91191 Gif-sur-Yvette Cedex (France)] [Institut de Physique Théorique, CE-Saclay, CEA, F-91191 Gif-sur-Yvette Cedex (France)

2014-02-28

336

Logarithmic conformal field theory approach to topologically massive gravity

We study the topologically massive gravity at the chiral point (chiral gravity) by using the logarithmic conformal field theory. Two new tensor fields of ?new and X are introduced for a candidate of propagating physical field at the chiral point. However, we show that (?new,?L) form a dipole ghost pair of unphysical fields and X is not a primary. This

Yun Soo Myung

2008-01-01

337

Multi-field inflation: Formulation, effective theory and phenomenology

NASA Astrophysics Data System (ADS)

We have described how to obtain the non-perturbative low energy effective field theory of single field inflation from a generic multi-field model by integrating out heavy fields. The features of heavy physics is described by the effective speed of sound, which leaves distinctive observational signatures in the correlation functions of the curvature perturbation.

Gong, J.-O.

2014-03-01

338

An application of neutrix calculus to quantum field theory

Neutrices are additive groups of negligible functions that do not contain any constants except 0. Their calculus was developed by van der Corput and Hadamard in connection with asymptotic series and divergent integrals. We apply neutrix calculus to quantum field theory, obtaining finite renormalizations in the loop calculations. For renormalizable quantum field theories, we recover all the usual physically observable results. One possible advantage of the neutrix framework is that effective field theories can be accommodated. Quantum gravity theories appear to be more manageable.

Y. Jack Ng; H. van Dam

2005-02-17

339

Introduction of a boundary in topological field theories

NASA Astrophysics Data System (ADS)

We study the consequences of the presence of a boundary in topological field theories in various dimensions. We characterize, univocally and on very general grounds, the field content and the symmetries of the actions which live on the boundary. We then show that these actions are covariant, despite appearances. We show also that physically relevant theories like the 2D Luttinger liquid model or the four-dimensional Maxwell theory, can be seen as boundary reductions of higher-dimensional topological field theories, which do not display local observables.

Amoretti, Andrea; Braggio, Alessandro; Caruso, Giacomo; Maggiore, Nicola; Magnoli, Nicodemo

2014-12-01

340

Entanglement entropy in Galilean conformal field theories and flat holography

We present the analytical calculation of entanglement entropy for a class of two dimensional field theories governed by the symmetries of the Galilean conformal algebra, thus providing a rare example of such an exact computation. These field theories are the putative holographic duals to theories of gravity in three-dimensional asymptotically flat spacetimes. We provide a check of our field theory answers by an analysis of geodesics. We also exploit the Chern-Simons formulation of three-dimensional gravity and adapt recent proposals of calculating entanglement entropy by Wilson lines in this context to find an independent confirmation of our results from holography.

Arjun Bagchi; Rudranil Basu; Daniel Grumiller; Max Riegler

2014-10-15

341

Entanglement entropy in Galilean conformal field theories and flat holography

We present the analytical calculation of entanglement entropy for a class of two dimensional field theories governed by the symmetries of the Galilean conformal algebra, thus providing a rare example of such an exact computation. These field theories are the putative holographic duals to theories of gravity in three-dimensional asymptotically flat spacetimes. We provide a check of our field theory answers by an analysis of geodesics. We also exploit the Chern-Simons formulation of three-dimensional gravity and adapt recent proposals of calculating entanglement entropy by Wilson lines in this context to find an independent confirmation of our results from holography.

Bagchi, Arjun; Grumiller, Daniel; Riegler, Max

2014-01-01

342

Pure Geometric Field Theory: Description of Gravity and Material Distribution

A field theory is constructed in the context of parameterized absolute parallelism\\linebreak geometry. The theory is shown to be a pure gravity one. It is capable of describing the gravitational field and a material distribution in terms of the geometric structure of the geometry used (the parallelization vector fields). Three tools are used to attribute physical properties to the geometric objects admitted by the theory. Poisson and Laplace equations are obtained in the linearized version of the theory. The spherically symmetric solution of the theory, in free space, is found to coincide with the Schwarzschild exterior solution of the general theory of relativity. The theory respects the weak equivalence principle in free space only. Gravity and material distribution are not minimally coupled.

M. I. Wanas; Nabil L. Youssef; W. El Hanafy

2014-07-21

343

Quantum Hall Physics Equals Noncommutive Field Theory

In this note, we study a matrix-regularized version of non-commutative U(1) Chern-Simons theory proposed recently by Polychronakos. We determine a complete minimal basis of exact wavefunctions for the theory at arbitrary level k and rank N and show that these are in one-to-one correspondence with Laughlin-type wavefunctions describing excitations of a quantum Hall droplet composed of N electrons at filling fraction 1/k. The finite matrix Chern-Simons theory is shown to be precisely equivalent to the theory of composite fermions in the lowest Landau level, believed to provide an accurate description of the filling fraction 1/k fractional quantum Hall state. In the large N limit, this implies that level k noncommutative U(1) Chern-Simons theory is equivalent to the Laughlin theory of the filling fraction 1k quantum Hall fluid, as conjectured recently by Susskind.

Rammsdonk , Mark van

2001-08-09

344

Relativistic field theory of neutron stars and their hyperon populations

The nuclear many-body problem is examined by means of the formulation of an effective relativistic field theory of interacting hadrons. A relativistic field theory of hadronic matter is especially appropriate for the description of hot or dense matter, because of the appearance of antiparticles and higher baryon resonances and because it automatically respects causality. 8 refs., 7 figs., 1 tab. (WRF)

Glendenning, N.K.

1986-01-01

345

Neurotransmitter Field Theory: A Composite Continuous and Discrete Model

Neurotransmitter Field Theory: A Composite Continuous and Discrete Model TR-CIS-0315-10 A Technical Report By Douglas S. Greer Mihran Tuceryan March 15, 2010 #12;1 Neurotransmitter Field Theory as an evolutionary extension of the endocrine system that transfixed the transmitter between cells and prevented

Tuceryan, Mihran

346

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed.

Jaekel, Christian D. [School of Mathematics, Cardiff University, Wales CF24 4AG (United Kingdom); Wreszinski, Walter F. [Departamento de Fisica Matematica, Instituto de Fisica, USP, Caixa Postal 66318, 05314-970 Sao Paulo (Brazil)

2011-01-15

347

NS-NS sector of closed superstring field theory

NASA Astrophysics Data System (ADS)

We give a construction for a general class of vertices in superstring field theory which include integration over bosonic moduli as well as the required picture changing insertions. We apply this procedure to find a covariant action for the NS-NS sector of Type II closed superstring field theory.

Erler, Theodore; Konopka, Sebastian; Sachs, Ivo

2014-08-01

348

Mean-field theory for Bose-Hubbard model under a magnetic field

We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.

Oktel, M. Oe.; Tanatar, B. [Department of Physics, Bilkent University, 06800 Bilkent, Ankara (Turkey); Nita, M. [Institute of Physics and Technology of Materials, P.O. Box MG7, Bucharest-Magurele (Romania)

2007-01-15

349

Relativistic theory for continuous measurement of quantum fields

We have proposed a formal theory for the continuous measurement of relativistic quantum fields. We have also derived the corresponding scattering equations. The proposed formalism reduces to known equations in the Markovian case. Two recent models for spontaneous quantum state reduction have been recovered in the framework of our theory. A possible example of the relativistic continuous measurement has been outlined in standard quantum electrodynamics. The continuous measurement theory possesses an alternative formulation in terms of interacting quantum and stochastic fields.

Diosi, L. (Central Research Institute for Physics, Budapest (Hungary))

1990-11-01

350

Incorporation of Generalized Uncertainty Principle into Lifshitz Field Theories

In this paper, we will incorporation the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bososnic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporation the generalized uncertainty principle into an non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations.

Mir Faizal; Barun Majumder

2014-08-17

351

Non-equilibrium conformal field theories with impurities

NASA Astrophysics Data System (ADS)

We present a construction of non-equilibrium steady states within conformal field theory. These states sustain energy flows between two quantum systems, initially prepared at different temperatures, whose dynamical properties are represented by two, possibly different, conformal field theories connected through an impurity. This construction relies on a real time formulation of conformal defect dynamics based on a field scattering picture parallelizingbut yet different fromthe Euclidean formulation. We present the basic characteristics of this formulation and give an algebraic construction of the real time scattering maps that we illustrate in the case of SU(2)-based conformal field theories.

Bernard, D.; Doyon, B.; Viti, J.

2015-02-01

352

An Algebraic Approach to Quantum Field Theory

It is shown that two quantum theories dealing, respectively, in the Hilbert spaces of state vectors H1 and H2 are physically equivalent whenever we have a faithful representation of the same abstract algebra of observables in both spaces, no matter whether the representations are unitarily equivalent or not. This allows a purely algebraic formulation of the theory. The framework of

Rudolf Haag; Daniel Kastler

1964-01-01

353

Effective field theory approach to quasi-single field inflation and effects of heavy fields

NASA Astrophysics Data System (ADS)

We apply the effective field theory approach to quasi-single field inflation, which contains an additional scalar field with Hubble scale mass other than inflaton. Based on the time-dependent spatial diffeomorphism, which is not broken by the time-dependent background evolution, the most generic action of quasi-single field inflation is constructed up to third order fluctuations. Using the obtained action, the effects of the additional massive scalar field on the primordial curvature perturbations are discussed. In particular, we calculate the power spectrum and discuss the momentum-dependence of three point functions in the squeezed limit for general settings of quasi-single field inflation. Our framework can be also applied to inflation models with heavy particles. We make a qualitative discussion on the effects of heavy particles during inflation and that of sudden turning trajectory in our framework.

Noumi, Toshifumi; Yamaguchi, Masahide; Yokoyama, Daisuke

2013-06-01

354

Bifurcation and dynamical symmetry breaking in a renormalization-group-improved field theory

NASA Astrophysics Data System (ADS)

We formulate the renormalization-group-improved theory for an mr?0 (massive) QCD Lagrangian. The Green's functions are parametrized in terms of two renormalization-group-invariant quantities, M0 and ?c. The theory exhibits usual analyticity structure for every M0>?ce1/6. In the limit M0=?ce1/6, mr becomes zero. The theory exhibits bifurcation in this limit, and chiral symmetry remains broken. is calculated in this limit.

Chang, Lay-Nam; Chang, Ngee-Pong

1985-06-01

355

Thermodynamics of String Field Theory Motivated Nonlocal Models

We investigate the thermodynamic properties of the nonlocal tachyon motivated by their nonlocal structure in string field theory. We use previously developed perturbative methods for nonlocal fields to calculate the partition function and the equation of state in the high temperature limit. We find that in these models the tachyons undergo a second order phase transition. We compare our results with those of ordinary scalar field theory. We also calculate the one loop finite temperature effective potential.

Tirthabir Biswas; Joseph Kapusta; Abraham Reddy

2012-01-07

356

Lagrangian Simulation of Combustion

A Lagrangian approach for the simulation of reactive flows has been developed during the course of this project, and has been applied to a number of significant and challenging problems including the transverse jet simulations. An efficient strategy for parallel domain decomposition has also been developed to enable the implementation of the approach on massively parallel architecture. Since 2005, we focused our efforts on the development of a semi-Lagrangian treatment of diffusion, and fast and accurate Lagrangian simulation tools for multiphysics problems including combustion.

Ahmed F. Ghoniem

2008-05-01

357

Darwin (1920) noted that when radiation can be neglected it should be possible to eliminate the radiation degrees-of-freedom from the action of classical electrodynamics and keep the discrete particle degrees-of-freedom only. Darwin derived his well known Lagrangian by series expansion in $v/c$ keeping terms up to order $(v/c)^2$. Since radiation is due to acceleration the assumption of low speed should not be necessary. A Lagrangian is suggested that neglects radiation without assuming low speed. It cures deficiencies of the Darwin Lagrangian in the ultra-relativistic regime.

Hanno Essen

2007-10-24

358

Deformations of Quantum Field Theories on Curved Spacetimes

The construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of globally hyperbolic spacetimes. First, we show that any four-dimensional spacetime which admits two commuting and spacelike Killing vector fields carries a family of wedge regions with causal properties analogous to the Minkowski space wedges. Deformations of quantum field theories on these spacetimes are carried out within the operator-algebraic framework - the emerging models share many structural properties with deformations of field theories on flat spacetime. In particular, deformed quantum fields are localized in the wedges of the considered spacetime. As a concrete example, the deformation of the free Dirac field is studied. Second, quantum field theories on de Sitter spacetime with global U(1) gauge symmetry are deformed using the joint action of the internal symmetry group and a one-parameter group of boosts. The resulting theories turn out to be wedge-local and non-isomorphic to the initial one for a class of theories, including the free charged Dirac field. The properties of deformed models coming from inclusions of CAR-algebras are studied in detail. Third, the deformation of the scalar free field in the Araki-Wood representation on Minkowski spacetime is discussed as a motivating example.

Eric Morfa-Morales

2012-02-15

359

Modeling Field Theory of Higher Cognitive Functions

The chapter discusses a mathematical theory of higher cognitive functions, including concepts, emotions, instincts, understanding, imagination and intuition. Mechanisms of the knowledge instinct are proposed, driving our understanding of the world. Aesthetic emotions and perception of beauty are related to \\

Leonid Perlovsky

2007-01-01

360

String field theory and tachyon dynamics

In this thesis we present some works done during my doctoral studies. These results focus on two directions. The first one is motivated by tachyon dynamics in open string theory. We calculate the stress tensors for the ...

Yang, Haitang, Ph. D. Massachusetts Institute of Technology

2006-01-01

361

Improving jet distributions with effective field theory.

We obtain perturbative expressions for jet distributions using soft-collinear effective theory (SCET). By matching SCET onto QCD at high energy, tree level matrix elements and higher order virtual corrections can be reproduced in SCET. The resulting operators are then evolved to lower scales, with additional operators being populated by required threshold matchings in the effective theory. We show that the renormalization group evolution and threshold matchings reproduce the Sudakov factors and splitting functions of QCD, and that the effective theory naturally combines QCD matrix elements and parton showers. The effective theory calculation is systematically improvable and any higher order perturbative effects can be included by a well-defined procedure. PMID:17155240

Bauer, Christian W; Schwartz, Matthew D

2006-10-01

362

Theory of Classical Higgs Fields. III. Metric-affine gauge theory

We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $P\\to X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/H\\to X$ are treated as classical Higgs fields. Its most comprehensive example is metric-affine gauge theory on the category of natural bundles where gauge fields are general linear connections on a manifold $X$, classical Higgs fields are arbitrary pseudo-Riemannian metrics on $X$, and matter fields are spinor fields. In particular, this is the case of gauge gravitation theory.

G. Sardanashvily; A. Kurov

2014-12-11

363

Mean Field Theory for Sigmoid Belief Networks

We develop a mean eld theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean eld theory provides a tractable approximation to the true probability dis-tribution in these networks; it also yields a lower bound on the likelihood of evidence. We demon-strate the utility of this framework on a benchmark problem in statistical pattern recognition|the classi cation

Lawrence K. Saul; Tommi Jaakkola; Michael I. Jordan

1996-01-01

364

Nonperturbative Matching for Field Theories with Heavy Fermions

We examine a paradox, suggested by Banks and Dabholkar, concerning nonperturbative effects in an effective field theory which is obtained by integrating out a generation of heavy fermions, where the heavy fermion masses arise from Yukawa couplings. They argue that light fermions in the effective theory appear to decay via instanton processes, whereas their decay is forbidden in the full theory. We resolve this paradox by showing that such processes in fact do not occur in the effective theory, due to matching corrections which cause the relevant light field configurations to have infinite action.

H. Georgi; L. Kaplan; D. Morin

1993-10-27

365

Perturbative Aspects of Low-Dimensional Quantum Field Theory

We investigate the low-dimensional applications of Quantum Field Theory (QFT), namely Chern-Simons-Witten Theory (CSWT) and Affine Toda Field Theory (ATFT) in 3- and 2- dimensions. We discuss the perturbative aspects of both theories and compare the results to the exact solutions obtained nonperturbatively. For the three dimensions CSWT case, the perturbative term agree with the nonperturbative polynomial invariants up to third order of the coupling constant 1/k. In the two dimensions ATFT, we investigate the perturbative aspect of S-matrices for A{sub 1}{sup (1)} case in eighth order of the coupling constant {beta}.

Wardaya, Asep Y. [Department of Physics, Diponegoro University, Jl. Prof. Soedarto SH, Semarang (Indonesia); Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, FMIPA, Institut Teknologi Bandung, Jl. Ganesha 10 Bandung 40132 (Indonesia); Zen, Freddy P.; Kosasih, Jusak S.; , Triyanta; Hartanto, Andreas [Indonesia Center for Theoretical and Mathematical Physics (ICTMP) (Indonesia); Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, FMIPA, Institut Teknologi Bandung, Jl. Ganesha 10 Bandung 40132 (Indonesia)

2010-06-22

366

Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions

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 co-variance, 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 $D = 2m$ 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 $D = 2m$. 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, $R \\sqrt{-g} = \\partial_j R^j$ 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.

Alexandre Yale; T. Padmanabhan

2010-08-30

367

Importance of the ?-FIELD in the Relativistic Mean Field Theory for Nuclear Matter

NASA Astrophysics Data System (ADS)

We generalize the Walecka model for nuclear matter by including the ?-field. It is found that a finite mean ?-field may lower the energy per nucleon even in the nuclear matter of subnormal density. A mean ?-field may significantly change the nuclear equation of state. The importance of considering the ?-field in the relativistic mean field theory for nuclear matter is therefore emphasized.

Zhang, Qi-Ren; Greiner, Walter

368

Some exact results on tachyon condensation in string field theory

The study of open string tachyon condensation in string field theory can be drastically simplified by making an appropriate choice of coordinates on the space of string fields. We show that a very natural coordinate system is suggested by the connection between the worldsheet renormalization group and spacetime physics. In this system only one field, the tachyon, condenses while all

David Kutasov; Marcos Marińo; Gregory Moore

2000-01-01

369

Quantum Simulation of Quantum Field Theories in Trapped Ions

We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.

Casanova, J.; Lamata, L. [Departamento de Quimica Fisica, Universidad del Pais Vasco-Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao (Spain); Egusquiza, I. L. [Departamento de Fisica Teorica, Universidad del Pais Vasco-Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao (Spain); Gerritsma, R.; Roos, C. F. [Institut fuer Quantenoptik und Quanteninformation, Oesterreichische Akademie der Wissenschaften, Otto-Hittmair-Platz 1, A-6020 Innsbruck (Austria); Institut fuer Experimentalphysik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria); Garcia-Ripoll, J. J. [Instituto de Fisica Fundamental, CSIC, Serrano 113-bis, 28006 Madrid (Spain); Solano, E. [Departamento de Quimica Fisica, Universidad del Pais Vasco-Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science, Alameda Urquijo 36, 48011 Bilbao (Spain)

2011-12-23

370

No resonant tunneling in standard scalar quantum field theory

We investigate the nature of resonant tunneling in Quantum Field Theory. Following the pioneering work of Banks, Bender and Wu, we describe quantum field theory in terms of infinite dimensional quantum mechanics and utilize the ``Most probable escape path'' (MPEP) as the class of paths which dominate the path integral in the classically forbidden region. Considering a 1+1 dimensional field theory example we show that there are five conditions that any associated bound state in the classically allowed region must satisfy if resonant tunnelling is to occur, and we then proceed to show that it is impossible to satisfy all five conditions simultaneously.

Edmund J. Copeland; Antonio Padilla; Paul M. Saffin

2007-09-03

371

Jordan cells in logarithmic limits of conformal field theory

It is discussed how a limiting procedure of conformal field theories may result in logarithmic conformal field theories with Jordan cells of arbitrary rank. This extends our work on rank-two Jordan cells. We also consider the limits of certain three-point functions and find that they are compatible with known results. The general construction is illustrated by logarithmic limits of (unitary) minimal models in conformal field theory. Characters of quasi-rational representations are found to emerge as the limits of the associated irreducible Virasoro characters.

Jorgen Rasmussen

2006-11-25

372

Impulsive Control of Lagrangian Systems and Locomotion in Fluids

Impulsive Control of Lagrangian Systems and Locomotion in Fluids Alberto Bressan Department. Aim of this paper is to provide a survey of the theory of impulsive control of Lagrangian systems. Then we discuss the analytical form taken by the equations of motion, and their impulsive character

Bressan, Alberto

373

Topological Quantum Field Theory via Chren-Simons Theory, part 1

To understand what does Chern-Simons with compact Lie group(does not like Dijkgraaf-Witten model with finite group in 3d) attach to a point, we first give a construction of Topological Quantum Field Theory(TQFT) via Chern-Simons theory in this paper. We discuss the Topological Quantum Field Theory and Chern-Simons theory via Category, then interpret the cobordism as cospan and field of space-time as span, which ultimately deduce the construction of TQFT.

Yifan Zhang; Ke Wu

2011-12-02

374

Topics in Lattice QCD and Effective Field Theory

Effective field theories provide a formalism for categorizing low-energy effects of a high-energy fundamental theory in terms of the low-energy degrees of freedom. This process has been well established in mapping the fundamental theory of QCD in terms of the hadronic degrees of freedom, which allows for quantitative connections and predictions between hardronic observables. A more direct approach to performing the non-perturbative QCD calculations is through lattice QCD. These computationally intensive calculations approximate continuum physics with a discretized lattice to extract hadronic phenomena from first principles. However, as in any approximation, there are multiple systematic errors between lattice QCD calculation and actual hardronic phenomena. To account for these systematic effects in terms of hadronic interactions, effective field theory proves to be useful. However, the fundamental theory of interest here is lattice QCD, as opposed to the usual continuum QCD. In this work, the basics of this process are outlined, and multiple original calculations are presented: effective field theory for anisotropic lattices, I=2 $\\pi\\pi$ scattering for isotropic, anisotropic, and twisted mass lattices. Additionally, a usage of effective field theories and the employment of an isospin chemical potential on the lattice is proposed to extract several computationally difficult scattering parameters. Lastly, recently proposed local, chiral lattice actions are analyzed in the framework of effective field theory, which illuminates various challenges in simulating such actions.

Michael I. Buchoff

2010-05-11

375

Heavy Quarks, QCD, and Effective Field Theory

The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E#11;ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e#11;ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi#12;eld theoretic de#12;nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.

Thomas Mehen

2012-10-09

376

Splitting fields and general differential Galois theory

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions. Bibliography: 14 titles.

Trushin, Dmitry V [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

2010-11-11

377

Rational SFT, linearized Legendrian contact homology, and Lagrangian Floer cohomology

We relate the version of rational Symplectic Field Theory for exact Lagrangian cobordisms introduced in [5] with linearized Legendrian contact homology. More precisely, if $L\\subset X$ is an exact Lagrangian submanifold of an exact symplectic manifold with convex end $\\Lambda\\subset Y$, where $Y$ is a contact manifold and $\\Lambda$ is a Legendrian submanifold, and if $L$ has empty concave end, then the linearized Legendrian contact cohomology of $\\Lambda$, linearized with respect to the augmentation induced by $L$, equals the rational SFT of $(X,L)$. Following ideas of P. Seidel, this equality in combination with a version of Lagrangian Floer cohomology of $L$ leads us to a conjectural exact sequence which in particular implies that if $X=\\C^{n}$ then the linearized Legendrian contact cohomology of $\\Lambda\\subset S^{2n-1}$ is isomorphic to the singular homology of $L$. We outline a proof of the conjecture and show how to interpret the duality exact sequence for linearized contact homology of [6] in terms of ...

Ekholm, Tobias

2009-01-01

378

NASA Astrophysics Data System (ADS)

The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of new Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation. Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed in a frame-independent setting. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance. The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT) experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in a real-time setting for the tropical cyclogenesis problem. Lagrangian diagnostics are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and {later a major hurricane.

Rutherford, B.; Montgomery, M. T.

2012-12-01

379

NASA Astrophysics Data System (ADS)

The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of new Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation. Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed objectively. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance. The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT) experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics developed here are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.

Rutherford, B.; Montgomery, M. T.

2011-12-01

380

NASA Astrophysics Data System (ADS)

The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation. Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed in a frame-independent setting. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance. The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT) experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.

Rutherford, B.; Montgomery, M. T.

2012-12-01

381

Topological Field Theory of Time-Reversal Invariant Insulators

We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.

Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.

2010-03-19

382

The Hilbert Lagrangian and Isometric Embedding: Tetrad Formulation of Regge-Teitelboim Gravity

We discuss Exterior Differential Systems (EDS) for the vacuum gravitational field. These EDS are derived by varying the Hilbert-Einstein Lagrangian, given most elegantly as a Cartan 4-forrm calibrating 4-spaces embedded in ten flat dimensions. In particular we thus formulate with tetrad equations the Regge-Teitelboim dynamics "a la string" (R-T); it arises when variation of the 4-spaces gives the Euler-Lagrange equations of a multicontact field theory. We calculate the Cartan character table of this EDS, showing the field equations to be well posed with no gauge freedom. The Hilbert Lagrangian as usually varied over just the intrinsic curvature structure of a 4-space yields only a subset of this dynamics, viz., solutions satisfying additional conditions constraining them to be Ricci-flat. In the static spherically symmetric case we present a new tetrad embedding in flat six dimensions, which allows reduction of the R-T field equations to a quadrature; the Schwarzschild metric is a special case. As has previously been noted there may be a classical correspondence of R-T theory with the hidden dimensions of brane theory, and perhaps this extended general relativistic dynamics holds in extreme circumstances where it can be interpreted as including a sort of dark or bulk energy, even though no term with a cosmological constant is included in the Lagrangian. As a multicontact system, canonical quantization should be straightforward.

Frank B. Estabrook

2009-08-03

383

Effective field theory for perturbations in dark energy and modified gravity

When recent observational evidence and the GR+FRW+CDM model are combined we obtain the result that the Universe is accelerating, where the acceleration is due to some not-yet-understood "dark sector". There has been a considerable number of theoretical models constructed in an attempt to provide an "understanding" of the dark sector: dark energy and modified gravity theories. The proliferation of modified gravity and dark energy models has brought to light the need to construct a "generic" way to parameterize the dark sector. We will discuss our new way of approaching this problem. We write down an effective action for linearized perturbations to the gravitational field equations for a given field content; crucially, our formalism does not require a Lagrangian to be presented for calculations to be performed and observational predictions to be extracted. Our approach is inspired by that taken in particle physics, where the most general modifications to the standard model are written down for a given field con...

Pearson, Jonathan A

2012-01-01

384

Effective field theory for perturbations in dark energy and modified gravity

When recent observational evidence and the GR+FRW+CDM model are combined we obtain the result that the Universe is accelerating, where the acceleration is due to some not-yet-understood "dark sector". There has been a considerable number of theoretical models constructed in an attempt to provide an "understanding" of the dark sector: dark energy and modified gravity theories. The proliferation of modified gravity and dark energy models has brought to light the need to construct a "generic" way to parameterize the dark sector. We will discuss our new way of approaching this problem. We write down an effective action for linearized perturbations to the gravitational field equations for a given field content; crucially, our formalism does not require a Lagrangian to be presented for calculations to be performed and observational predictions to be extracted. Our approach is inspired by that taken in particle physics, where the most general modifications to the standard model are written down for a given field content that is compatible with some assumed symmetry (which we take to be isotropy of the background spatial sections).

Jonathan A. Pearson

2012-05-16

385

Quantum field theory as eigenvalue Arnold Neumaier

, multiparticle Dirac equation, Ehrenfest equation, eigenvalue problem, electrodynamics, Euclidean Poisson algebra to the laws of mathematics . . . Isaac Newton, 1686 [30] Renormalized quantum electrodynamics is by far the most successful theory we have today. This very impressive fact, however, does not make the whole

Neumaier, Arnold

386

A New Lorentz Violating Nonlocal Field Theory From String-Theory

A four-dimensional field theory with a qualitatively new type of nonlocality is constructed from a setting where Kaluza-Klein particles probe toroidally compactified string theory with twisted boundary conditions. In this theory fundamental particles are not pointlike and occupy a volume proportional to their R-charge. The theory breaks Lorentz invariance but appears to preserve spatial rotations. At low energies, it is approximately N=4 Super Yang-Mills theory, deformed by an operator of dimension seven. The dispersion relation of massless modes in vacuum is unchanged, but under certain conditions in this theory, particles can travel at superluminal velocities.

Ganor, Ori J.

2007-10-04

387

NASA Astrophysics Data System (ADS)

A short range tracer experiment was carried out under fair-weather conditions over prealpine complex terrain in Switzerland. The prevailing wind direction in the troposphere over the Swiss Plateau was characterized by a northeasterly flow condition that is called bise in Switzerland. This wind system is oriented along the Swiss Plateau due to channelling effects between the Alps in the south and the Jura mountains in the north. Over the prealpine experiment area, however, the SODAR measurements gave evidence of the presence of a thermally driven wind system with a diurnal cycle. The air pollution dispersion scenario of the tracer experiment was simulated by a Lagrangian air quality model for passive air constituents called PARTRAC. The calculated data were compared to the measured tracer concentrations. PARTRAC requires 3D-flow fields which were either generated diagnostically by the mass consistent wind model CONDOR, or prognostically by the non-hydrostatic mesoscale meteorological model MEMO. The sensitivity of the CONDOR wind fields to varying input of measured wind data was investigated by comparing the calculated concentration fields to observational data. The reliability of the concentration predictions was assessed on the basis of statistical performance measures by comparing the predicted half-hourly concentrations to the corresponding measured data paired at equal locations and times. This sensitivity study was aimed at providing PARTRAC with the most representative diagnostic flow fields in order to numerically reproduce the observations as reliably as possible and to establish a benchmark to which the prognostic modelling results were compared in a second step. The prognostic flow fields were generated by a passive model nesting technique in order to reproduce the thermally driven diurnal flow circulation between the prealpine part of the Swiss Plateau and the Alps. The occurrence of this wind regime was suggested by the SODAR measurements and by the dispersion model results relying on the diagnostic wind fields. The initial conditions for the prognostic model MEMO were delivered by a regional weather forecast model that is in operation both at the weather services in Germany (DWD) and Switzerland (SMA). As will be demonstrated in the first part of this paper, the diagnostic transport and dispersion modelling does not necessarily produce a reliable description of an air pollution episode over complex terrain, such as the Swiss Plateau. Therefore, the density of the permanently operating network of weather stations in SwitzerlandANETZ and ENETdefinitely appears to be too small to be considered as a sufficient data base for reliable diagnostic concentration predictions in the case of an emergency situation. On the other hand, the prognostic mesoscale modelling of flow fields in complex terrain suffers from the same deficiency as the diagnostic approach inasmuch as reliable results often require a sensitivity study with the nesting of flow fields originating from different meteorological processes at different scales. Therefore, the data selection for such a grid nesting procedure requires a phenomenological knowledge of the different meteorological processes involved. In the case of MEMO at the time of this study, this data selection could be accomplished in different ways, which did not necessarily produce always identical results.

Lamprecht, R.; Berlowitz, D.

388

Theory of plasma confinement in non-axisymmetric magnetic fields

NASA Astrophysics Data System (ADS)

The theory of plasma confinement by non-axisymmetric magnetic fields is reviewed. Such fields are used to confine fusion plasmas in stellarators, where in contrast to tokamaks and reversed-field pinches the magnetic field generally does not possess any continuous symmetry. The discussion is focussed on magnetohydrodynamic equilibrium conditions, collisionless particle orbits, and the kinetic theory of equilbrium and transport. Each of these topics is fundamentally affected by the absence of symmetry in the magnetic field: the field lines need not trace out nested flux surfaces, the particle orbits may not be confined, and the cross-field transport can be very large. Nevertheless, by tailoring the magnetic field appropriately, well-behaved equilibria with good confinement can be constructed, potentially offering an attractive route to magnetic fusion. In this article, the mathematical apparatus to describe stellarator plasmas is developed from first principles and basic elements underlying confinement optimization are introduced.

Helander, Per

2014-08-01

389

The Monte Carlo method in quantum field theory

This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo method with Markov-chain based importance sampling is presented. Properties of Markov chains are discussed in detail and several proofs are presented, culminating in the fundamental limit theorem for irreducible Markov chains. The example of a real scalar field theory is used to illustrate the Metropolis-Hastings method and to demonstrate the effectiveness of an action-preserving (microcanonical) local updating algorithm in reducing autocorrelations. The goal of these lectures is to provide the beginner with the basic skills needed to start carrying out Monte Carlo studies in quantum field theories, as well as to present the underlying theoretical foundations of the method.

Colin Morningstar

2007-02-20

390

Towards an invariant geometry of double field theory

We introduce a geometrical framework for double field theory in which generalized Riemann and torsion tensors are defined without reference to a particular basis. This invariant geometry provides a unifying framework for ...

Hohm, Olaf

391

Estimating perturbative coefficients in quantum field theory and statistical physics

NASA Astrophysics Data System (ADS)

We present a method for estimating perturbative coefficients in quantum field theory and statistical physics. We are able to obtain reliable error bars for each estimate. The results are in excellent agreement with known exact calculation.

Samuel, Mark A.

1995-07-01

392

Semi-Classical Field Theory as Decoherence Free Subspaces

We formulate semi-classical field theory as an approximate decoherence-free-subspace of a finite-dimensional quantum-gravity hilbert space. A complementarity construction can be realized as a unitary transformation which changes the decoherence-free-subspace. This can be translated to signify that field theory on a global slice, in certain space-times, is the simultaneous examination of two different superselected sectors of a field theory. We posit that a correct course graining procedure of quantum gravity should be WKB states propagating in a curved background in which particles exiting a horizon have imaginary components to their phases. The field theory appears non-unitary, but it is due to the existence of approximate decoherence free sub-spaces. Furthermore, the importance of operator spaces in the course-graining procedure is discussed. We also briefly touch on Firewalls.

Jaime Varela

2014-05-07

393

Exactly stable collective oscillations in conformal field theory

Any conformal field theory (CFT) on a sphere supports completely undamped collective oscillations. We discuss the implications of this fact for studies of thermalization using AdS/CFT. Analogous oscillations occur in ...

Freivogel, Benjamin W.

394

Field theory of the quantum Hall nematic transition

NASA Astrophysics Data System (ADS)

The topological physics of quantum Hall states is efficiently encoded in purely topological quantum field theories of the Chern-Simons type. The reliable inclusion of low-energy dynamical properties in a continuum description, however, typically requires proximity to a quantum critical point. We construct a field theory that describes the quantum transition from an isotropic to a nematic Laughlin liquid. The soft mode associated with this transition approached from the isotropic side is identified as the familiar intra-Landau level Girvin-MacDonald-Platzman mode. We obtain z=2 dynamic scaling at the critical point and a description of Goldstone and defect physics on the nematic side. Despite the very different physical motivation, our field theory is essentially identical to a recent geometric field theory for a Laughlin liquid proposed by Haldane.

Maciejko, J.; Hsu, B.; Kivelson, S. A.; Park, YeJe; Sondhi, S. L.

2013-09-01

395

The Goldstone fields of interacting higher spin field theory on AdS(4)

A higher spin field theory on AdS(4) possesses a conformal field theory on the boundary R(3) which can be identified with the critical O(N) sigma model of O(N) invariant fields only. The notions of quasiprimary and secondary fields can be carried over to the AdS theory. If de Donder's gauge is applied, the traceless part of the higher spin field on AdS(4) is quasiprimary and the Goldstone fields are quasiprimary fields to leading order, too. Those fields corresponding to the Goldstone fields in the critical O(N) sigma model are odd rank symmetric tensor currents which vanish in the free field limit.

Werner Ruehl

2006-07-25

396

Dual path integral representation for finite temperature quantum field theory

We impose the periodicity conditions corresponding to the Matsubara formalism for thermal field theory as constraints in the imaginary-time path integral. These constraints are introduced by means of time-independent auxiliary fields which, by integration of the original variables, become dynamical fields in the resulting 'dual' representation for the theory. This alternative representation has the appealing property of involving fields that live in one dimension less than the original ones, with a quantum partition function whose integration measure is identical to the one of its classical counterpart, albeit with a different (spatially nonlocal) action.

Ttira, C. Ccapa; Fosco, C. D. [Centro Atomico Bariloche and Instituto Balseiro, Comision Nacional de Energia Atomica, 8400 Bariloche (Argentina); Malbouisson, A. P. C.; Roditi, I. [Centro Brasileiro de Pesquisas Fisicas-CBPF/MCT Rua Dr. Xavier Sigaud, 150, 22290-180 Rio de Janeiro, RJ (Brazil)

2008-05-15

397

Thermodynamics and Finite size scaling in Scalar Field Theory

Thermodynamics and Finite size scaling in Scalar Field Theory A thesis submitted to the Tata Research, Mumbai December 2008 #12;ii #12;Synopsis In this work we study the thermodynamics of an interacting 4 theory in 4 space- time dimensions. The expressions for the thermodynamic quantities are worked

398

Relativistic theory for continuous measurement of quantum fields

We have proposed a formal theory for the continuous measurement of relativistic quantum fields. We have also derived the corresponding scattering equations. The proposed formalism reduces to known equations in the Markovian case. Two recent models for spontaneous quantum state reduction have been recovered in the framework of our theory. A possible example of the relativistic continuous measurement has been

L. Diósi

1990-01-01

399

Development of field theory in the last 50 years

This article is devoted to the development of quantum field theory, a discipline that began with quantum electrodynamics which was born in 1927 when P. A. M. Dirac published his famous paper ''The Quantum Theory of the Emission and Absorption of Radiation.''

Weisskopf, V.F.

1981-11-01

400

Development of field theory in the last 50 years

This article is devoted to the development of quantum field theory, a discipline that began with quantum electrodynamics which was born in 1927 when P. A. M. Dirac published his famous paper ''The Quantum Theory of the Emission and Absorption of Radiation.''

Victor F. Weisskopf

1981-01-01

401

Quasi-Particles in Non-Commutative Field Theory

After a short introduction to the UV/IR mixing in non-commutative field theories we review the properties of scalar quasi-particles in non-commutative supersymmetric gauge theories at finite temperature. In particular we discuss the appearance of super-luminous wave propagation.

Landsteiner, K

2000-01-01

402

Quasi-Particles in Non-Commutative Field Theory

After a short introduction to the UV/IR mixing in non-commutative field theories we review the properties of scalar quasi-particles in non-commutative supersymmetric gauge theories at finite temperature. In particular we discuss the appearance of super-luminous wave propagation.

Karl Landsteiner

2000-11-01

403

Elementary Particles of Conventional Field Theory as Regge Poles

Composite states in nonrelativistic scattering theory lie on Regge ; trajectories corresponding to poles in the angular momentum plane that move with ; varying energy. Composite particles in relativistic field theory are believed to ; have the same behavior. According to the Regge pole hypothesis, particles like ; the nucleon also lie on Regge trajectories. An investigition is made to

M. Gell-Mann; M. L. Goldberger

1962-01-01

404

Spectra of Conformal Field Theories with Current Algebras

This is an elementary review of our recent work on the classification of the spectra of those two-dimensional rational conformal field theories (RCFTs) whose (maximal) chiral algebras are current algebras. We classified all possible partition functions for such theories when the defining finite-dimensional Lie algebra is simple. The concepts underlying this work are emphasized, and are illustrated using simple examples.

T. Gannon; P. Ruelle; M. A. Walton

1995-11-13

405

Logarithmic conformal field theory approach to topologically massive gravity

We study the topologically massive gravity at the chiral point (chiral gravity) by using the logarithmic conformal field theory. Two new tensor fields of $\\psi^{new}$ and $X$ are introduced for a candidate of propagating physical field at the chiral point. However, we show that ($\\psi^{new},\\psi^L$) form a dipole ghost pair of unphysical fields and $X$ is not a primary. This implies that there is no physically propagating degrees of freedom at the chiral point.

Yun Soo Myung

2008-08-14

406

Effective field theories of baryons and mesons, or, what do quarks do?

This thesis is an attempt to understand the properties of the protons, pions and other hadrons in terms of their fundamental building blocks. In the first chapter the author reviews several of the approaches that have already been developed. The Nambu-Jona-Lasinio model offers the classic example of a derivation of meson properties from a quark Lagrangian. The chiral quark model encodes much of the intuition acquired in recent decades. The author also discusses the non-linear sigma model, the Skyrme model, and the constituent quark model, which is one of the oldest and most successful models. In the constituent quark model, the constituent quark appears to be different from the current quark that appears in the fundamental QCD Lagrangian. Recently it was proposed that the constituent quark is a topological soliton. In chapter 2 the author investigates this soliton, calculating its mass, radius, magnetic moment, color magnetic moment, and spin structure function. Within the approximations used, the magnetic moments and spin structure function cannot simultaneously be made to agree with the constituent quark model. In chapter 3 the author uses a different plan of attack. Rather than trying to model the constituents of the baryon, he begins with an effective field theory of baryons and mesons, with couplings and masses that are simply determined phenomenologically. Meson loop corrections to baryon axial currents are then computed in the 1/N expansion. It is already known that the one-loop corrections are suppressed by a factor 1/N; here it is shown that the two-loop corrections are suppressed by 1/N{sup 2}. To leading order, these corrections are exactly the same as would be calculated in the constituent quark model. This method therefore offers a different approach to the constituent quark.

Keaton, G.L. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group

1995-06-26

407

Quantum field theory in quantum set algebra

A modular quantum architecture is given for the space-time, particles, and fields of the Standard Model and General Relativity. It assumes a right-handed neutrino, so that based on their multiplet structure all fundamental fermions have isospin 1/2. This opens the possibility that the Higgs field can be identified with the Yang $i$-field of 1947. The quantum gravitational metric form proposed is a quantification of the Killing form of the quantum space-time cell. There is no trace of the black hole phenomenon at the one-cell quantum level.

David Ritz Finkelstein

2014-03-14

408

Algebraic solutions in Open String Field Theory - a lightning review

In this short talk we review basic ideas of string field theory with the emphasis on the recent developments. We show how without much technicalities one could look for analytic solutions to Witten's open string field theory. This is an expanded version of a talk given by the author over the last year at number of occasions and notably at the conference "Selected Topics in Mathematical and Particle Physics" in honor of Prof. Jiri Niederle 70th birthday.

Schnabl, Martin

2010-01-01

409

Algebraic solutions in Open String Field Theory - a lightning review

In this short talk we review basic ideas of string field theory with the emphasis on the recent developments. We show how without too much technicality one can look for analytic solutions to Witten's open string field theory. This is an expanded version of a talk given by the author over the last year at a number of occasions and notably at the conference "Selected Topics in Mathematical and Particle Physics" in honor of Prof. Jiri Niederle's 70th birthday.

Martin Schnabl

2010-04-27

410

Non-commutative geometry and string field theory

An attempt is made to interpret the interactions of bosonic open strings as defining a non-cummulative, associative algebra, and to formulate the classical non-linear field theory of such strings in the language of non-commulative geometry. The point of departure is the BRST approach to string field theory. A setting is given in which there is a unique gauge invariant action,

Edward Witten

1986-01-01

411

The Large N Limit of Superconformal Field Theories and Supergravity

We show that the large $N$ limit of certain conformal field theories in\\u000avarious dimensions include in their Hilbert space a sector describing\\u000asupergravity on the product of Anti-deSitter spacetimes, spheres and other\\u000acompact manifolds. This is shown by taking some branes in the full M\\/string\\u000atheory and then taking a low energy limit where the field theory on the

Juan M. Maldacena

1997-01-01

412

KK-masses in dipole deformed field theories

We reconsider aspects of non-commutative dipole deformations of field theories. Among our findings there are hints to new phases with spontaneous breaking of translation invariance (stripe phases), similar to what happens in Moyal-deformed field theories. Furthermore, using zeta-function regularization, we calculate quantum corrections to KK-state masses. The corrections coming from non-planar diagrams show interesting but non-universal behaviour. Depending on the

Karl Landsteiner; Sergio Montero

2006-01-01

413

General structure of classical reparametrization-invariant matter systems, mainly the relativistic particle and its $d$-brane generalization, are studied. The exposition is in close analogy with the relativistic particle in an electromagnetic field as reparametrization-invariant system. The structure of a diffeomorphism invariant Lagrangian action for an extended object ($d$-brane) embedded in a bulk space M is discussed. Our construction uses first order homogeneous Lagrangians to achieve general covariance in contrast to the constructions that use scalar Lagrangians along with metric dependent integration measure. The framework contains intrinsically the relativistic point particle, string theory, and Dirac-Nambu-Goto Lagrangians. In a natural way, the matter Lagrangian contains background interaction fields, such as a 1-form field, analogous to the electromagnetic vector potential, and a metric tensor. The framework naturally suggests new classical interaction fields beyond electromagnetism and gravity. Construction of aninteraction field Lagrangian that is background free and consistent with the gauge symmetries presented in the equations of motion for the matter is outlined. Keywords: diffeomorphism invariant systems, reparametrization-invariant matter systems, matter Lagrangian, homogeneous singular Lagrangians, relativistic particle, string theory, extended objects, d-branes, interaction fields, classical forces beyond electromagnetism and gravity, generally covariant theory, gauge symmetries, background free theories.

V. G. Gueorguiev

2005-12-22

414

Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory

I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.

H. Nikolic

2006-10-12

415

Solar magnetic fields and the dynamo theory

Unlike Earths dipolar magnetic fields, solar magnetic fields consist of wide ranges of length-scales and strengths, and interestingly, they evolve in a cyclic fashion with a 22-year periodicity. A magnetohydrodynamic dynamo operating in the Sun is most likely responsible for producing the solar magnetic activity cycle. While the first solar dynamo models were built half a century ago, recent views

M. Dikpati

2005-01-01

416

Nonlinear Response from Transport Theory and Quantum Field Theory at Finite Temperature

We study nonlinear response in weakly coupled hot $\\phi^4$ theory. We obtain an expression for a quadratic shear viscous response coefficient using two different formalisms: transport theory and response theory. The transport theory calculation is carried out by assuming a local equilibrium form for the distribution function and expanding in the gradient of the local four dimensional velocity field. By doing a gradient expansion on the Boltzmann equation we obtain a hierarchy of equations for the coefficients of this expansion.To do the response theory calculation we use Zubrave's techniques in nonequilibrium statistical mechanics to derive a generalized Kubo formula. Using this formula allows us to obtain the quadratic shear viscous response from the three-point retarded green function of the viscous shear stress tensor. We use the closed time path formalism of real time finite temperature field theoryto show that this three-point function can be calculated using equilibrium quantum field theory by writing i...

Carrington, M E; Kobes, R L; Defu, Hou

2001-01-01

417

Abelian Chern{endash}Simons theory. I. A topological quantum field theory

We give a construction of the Abelian Chern{endash}Simons gauge theory from the point of view of a 2+1-dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas that have been previously explored in connection to the non-Abelian Chern{endash}Simons theory [J. Diff. Geom. {bold 33}, 787{endash}902 (1991); Topology {bold 32}, 509{endash}529 (1993)]. We formulate the topological quantum field theory in terms of the category of extended 2- and 3-manifolds introduced in a preprint by Walker in 1991 and prove that it satisfies the axioms of unitary topological quantum field theories formulated by Atiyah [Publ. Math. Inst. Hautes Etudes Sci. Pans {bold 68}, 175{endash}186 (1989)]. {copyright} {ital 1998 American Institute of Physics.}

Manoliu, M. [Department of Mathematics, University of Texas, Austin, Texas 78712 (United States)] [Department of Mathematics, University of Texas, Austin, Texas 78712 (United States)

1998-01-01

418

Conformal field theories with infinitely many conservation laws

Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, 'Unitary positive energy representations of scalar bilocal fields,' Commun. Math. Phys. 271, 223-246 (2007); e-print arXiv:math-ph/0604069v3; and 'Infinite dimensional Lie algebras in 4D conformal quantum field theory,' J. Phys. A Math Theor. 41, 194002 (2008); e-print arXiv:0711.0627v2 [hep-th

Todorov, Ivan [Institut des Hautes Etudes Scientifiques F-91440, Bures-sur-Yvette (France)] [Institut des Hautes Etudes Scientifiques F-91440, Bures-sur-Yvette (France)

2013-02-15

419

BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons--kinks, vortices, and magnetic monopoles--and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is a tall order for a single chapter, relying rather heavily on additional background knowledge (for example supersymmetry) that students will not have unless they have already studied these topics in some depth. At this point students will need to be content with either appreciating the results as presented or else going to the original source material. The last four chapters of the book deal with anomalies and instantons, and again the reader is led from the simple material to the complex in a straightforward manner. Students should be able to follow the discussion both quantitatively and qualitatively, and become well-versed in understanding the 'big picture' provided they work through the material. The discussion on vacuum decay near the end of the book is quite timely given recent developments in eternal inflations, cosmic bubbles, and the like. The book contains a nice appendix that introduces students to the elements of Lie groups and Lie algebras that are required to understand a number of the ideas presented in various places in the book. There is also a short appendix on index theorems that should at least given students a basic sense of how these methods are employed in the subject at hand. This book would make a useful textbook for a mid-level graduate course. Though a bit terse in places, all of the main elements are there, in terms of both concept and methodology. It would make a fine addition to the library of any theorist in high-energy physics, gravitation, or cosmology.

Mann, Robert

2013-02-01

420

Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

NASA Astrophysics Data System (ADS)

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N?3 part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.

Asano, Masako

2013-03-01

421

Accretion disks and dynamos: toward a unified mean field theory

NASA Astrophysics Data System (ADS)

Conversion of gravitational energy into radiation near stars and compact objects in accretion disks and the origin of large-scale magnetic fields in astrophysical rotators have often been distinct topics of active research in astrophysics. In semi-analytic work on both problems it has been useful to presume large-scale symmetries, which necessarily results in mean field theories; magnetohydrodynamic turbulence makes the underlying systems locally asymmetric and highly nonlinear. Synergy between theory and simulations should aim for the development of practical, semi-analytic mean field models that capture the essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion disk theory have exemplified such ongoing pursuits. Twenty-first century MFD theory has more nonlinear predictive power compared to 20th century MFD theory, whereas alpha-viscosity accretion theory is still in a 20th century state. In fact, insights from MFD theory are applicable to accretion theory and the two are really artificially separated pieces of what should ultimately be a single coupled theory. I discuss pieces of progress that provide clues toward a unified theory. A key concept is that large-scale magnetic fields can be sustained via local or global magnetic helicity fluxes or via relaxation of small-scale magnetic fluctuations, without appealing to the traditional kinetic helicity driver of 20th century textbooks. These concepts may help explain the formation of large-scale fields that supply non-local angular momentum transport via coronae and jets in a unified theory of accretion and dynamos. In diagnosing the role of helicities and helicity fluxes in disk simulations, it is important to study each disk hemisphere separately to avoid being potentially misled by the cancelation that occurs as a result of reflection asymmetry. The fraction of helical field energy in disks is expected to be small compared to the total field in each hemisphere as a result of shear, but can still play a fundamental role in large-scale dynamo action.

Blackman, Eric G.

2012-11-01

422

The Consistency of Causal Quantum Geometrodynamics and Quantum Field Theory

We consider quantum geometrodynamics and parametrized quantum field theories in the framework of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work [1], where a hamiltonian formalism for the bohmian trajectories was constructed, we show the consistency of the theory for any quantum potential, completing the scenarios for canonical quantum cosmology presented there. In the latter case, we prove the consistency of scalar field theory in Minkowski spacetime for any quantum potential, and we show, using this alternative hamiltonian method, a concrete example where Lorentz invariance of individual events is broken.

N. Pinto-Neto; E. Sergio Santini

2000-09-22

423

Black Holes as Conformal Field Theories on Horizons

We show that any nonextreme black hole can be described by a state with $L_0=E_R$ in a $D=2$ chiral conformal field theory with central charge $c=12E_R$ where $E_R$ is the dimensionless Rindler energy of the black hole. The theory lives in the very near horizon region, i.e. around the origin of Rindler space. Black hole hair is the momentum along the Euclidean dimensionless Rindler time direction. As evidence, we show that $D$--dimensional Schwarzschild black holes and $D=2$ dilatonic ones that are obtained from them by spherical reduction are described by the same conformal field theory states.

Halyo, Edi

2015-01-01

424

Kohn-Sham Theory in the Presence of Magnetic Field

In the well-known Kohn-Sham theory in Density Functional Theory, a fictitious non-interacting system is introduced that has the same particle density as a system of $N$ electrons subjected to mutual Coulomb repulsion and an external electric field. For a long time, the treatment of the kinetic energy was not correct and the theory was not well-defined for $N$-representable particle densities. In the work of [Hadjisavvas and Theophilou, Phys. Rev. A, 1984, 30, 2183], a rigorous Kohn-Sham theory for $N$-representable particle densities was developed using the Levy-Lieb functional. Since a Levy-Lieb-type functional can be defined for Current Density Functional Theory formulated with the paramagnetic current density, we here develop a rigorous $N$-representable Kohn-Sham approach for interacting electrons in magnetic field. Furthermore, in the one-electron case, criteria for $N$-representable particle densities to be $v$-representable are given.

Andre Laestadius

2014-04-11

425

Sections, multisections, and U(1) fields in F-theory

We show that genus-one fibrations lacking a global section fit naturally into the geometric moduli space of Weierstrass models. Elliptic fibrations with multiple sections (nontrivial Mordell-Weil rank), which give rise in F-theory to abelian U(1) fields, arise as a subspace of the set of genus-one fibrations with multisections. Higgsing of certain matter multiplets charged under abelian gauge fields in the corresponding supergravity theories break the U(1) gauge symmetry to a discrete gauge symmetry group. We further show that in six dimensions every U(1) gauge symmetry arising in an F-theory model can be found by Higgsing an SU(2) gauge symmetry with adjoint matter, and that a similar structure holds for F-theory geometries giving 4D supergravity theories.

David R. Morrison; Washington Taylor

2014-09-30

426

SUSY gauge theory on graded manifolds

Lagrangian classical field theory of even and odd fields is adequately formulated in terms of fibre bundles and graded manifolds. In particular, conventional Yang-Mills gauge theory is theory of connections on smooth principal bundles, but its BRST extension involves odd ghost fields an antifields on graded manifolds. Here, we formulate Yang-Mills theory of Grassmann-graded gauge fields associated to Lie superalgebras on principal graded bundles. A problem lies in a geometric definition of odd gauge fields. Our goal is Yang--Mills theory of graded gauge fields and its BRST extension.

G. Sardanashvily; W. Wachowski

2014-06-24

427

The principle of stationary nonconservative action for classical mechanics and field theories

We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial value formulation of physical problems and allows for time-irreversible processes, such as dissipation, to be included at the level of the action. In this formalism, the equations of motion are generated by extremizing a nonconservative action $\\mathcal{S}$, which is a functional of a doubled set of degrees of freedom. The corresponding nonconservative Lagrangian contains a potential $K$ which generates nonconservative forces and interactions. Such a nonconservative potential can arise in several ways, including from an open system interacting with inaccessible degrees of freedom or from integrating out or coarse-graining a subset of variables in closed systems. We generalize Noether's theorem to show how Noether currents are modified and no longer conserved when $K$ is non-vanishing. Consequently, the nonconservative aspects of a physical system are derived solely from $K$. We show how to use the formalism with examples of nonconservative actions for discrete systems including forced damped harmonic oscillators, radiation reaction on an accelerated charge, and RLC circuits. We present examples for nonconservative classical field theories. Our approach naturally allows for irreversible thermodynamic processes to be included in an unconstrained variational principle. We present the nonconservative action for a Navier-Stokes fluid including the effects of viscous dissipation and heat diffusion, as well as an action that generates the Maxwell model for viscoelastic materials, which can be easily generalized to more realistic rheological models. We show that the nonconservative action can be derived as the classical limit of a more complete quantum theory.

Chad R. Galley; David Tsang; Leo C. Stein

2014-12-09

428

Logarithmic correlators in nonrelativistic conformal field theory

We show how logarithmic terms may arise in the correlators of fields which belong to the representation of the Schroedinger-Virasoro algebra or the affine Galilean conformal algebra (GCA). We show that in GCA, only scaling operator can have a Jordan form and rapidity cannot. We observe that in both algebras, logarithmic dependence appears along the time direction alone.

Hosseiny, Ali; Rouhani, Shahin [Department of Physics, Sharif University of Technology, Tehran 11165-9161 (Iran, Islamic Republic of)

2010-10-15

429

Interactive Courseware for Teaching Field Theory

Today lectures often are accompanied by web publications of the courses where students can recapitulate the material enriched by additional information and links. For technical fields, complex mathematical formulas have to be published on the web, up to now a problem. We present a new course management system that uses new techniques of web based publishing like MathML in order

Johannes Görke; Michael H. W. Hoffmann

430

Symmetry restoration in a theory of a self-interacting charged scalar field at finite temperature and in the presence of an external magnetic field is examined. The effective potential is evaluated nonperturbatively in the context of the optimized perturbation theory method. It is explicitly shown that in all ranges of the magnetic field, from weak to large fields, the phase transition is second order and that the critical temperature increases with the magnetic field. In addition, we present an efficient way to deal with the sum over the Landau levels, which is of interest especially in the case of working with weak magnetic fields.

Duarte, D. C.; Farias, R. L. S. [Departamento de Ciencias Naturais, Universidade Federal de Sao Joao Del Rei, 36301-000, Sao Joao Del Rei, MG (Brazil); Ramos, Rudnei O. [Departamento de Fisica Teorica, Universidade do Estado do Rio de Janeiro, 20550-013 Rio de Janeiro, RJ (Brazil)

2011-10-15

431

Analytic solution for tachyon condensation in open string field theory

We propose a new basis in Witten's open string field theory, in which the star product simplifies considerably. For a convenient choice of gauge the classical string field equation of motion yields straightforwardly an exact analytic solution that represents the nonperturbative tachyon vacuum. The solution is given in terms of Bernoulli numbers and the equation of motion can be viewed

Martin Schnabl

2005-01-01

432

Dynamical symmetry breaking in asymptotically free field theories

Two-dimensional massless fermion field theories with quartic interactions are analyzed. These models are asymptotically free. The models are expanded in powers of 1N, where N is the number of components of the fermion field. In such an expansion one can explicitly sum to all orders in the coupling constants. It is found that dynamical symmetry breaking occurs in these models

David J. Gross; André Neveu

1974-01-01

433

Cold atom simulation of interacting relativistic quantum field theories

We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.

J. Ignacio Cirac; Paolo Maraner; Jiannis K. Pachos

2010-10-04

434

New dynamical mean-field dynamo theory and closure approach.

We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, E. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of E is coupled into the theory. The solutions predict significant field growth in a kinematic phase and a saturation rate/strength that is magnetic Reynolds number dependent/independent in agreement with numerical simulations. The amplitude of early time oscillations provides a diagnostic for the closure. PMID:12484833

Blackman, Eric G; Field, George B

2002-12-23

435

Long-range interactions in lattice field theory

Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.

Rabin, J.M.

1981-06-01

436

Energy Inequalities in Quantum Field Theory

Quantum fields are known to violate all the pointwise energy conditions of classical general relativity. We review the subject of quantum energy inequalities: lower bounds satisfied by weighted averages of the stress-energy tensor, which may be regarded as the vestiges of the classical energy conditions after quantisation. Contact is also made with thermodynamics and related issues in quantum mechanics, where such inequalities find analogues in sharp Gaarding inequalities.

Christopher J. Fewster

2005-01-31

437

Algebraic geometry informs perturbative quantum field theory

Single-scale Feynman diagrams yield integrals that are periods, namely projective integrals of rational functions of Schwinger parameters. Algebraic geometry may therefore inform us of the types of number to which these integrals evaluate. We give examples at 3, 4 and 6 loops of massive Feynman diagrams that evaluate to Dirichlet $L$-series of modular forms and examples at 6, 7 and 8 loops of counterterms that evaluate to multiple zeta values or polylogarithms of the sixth root of unity. At 8 loops and beyond, algebraic geometry informs us that polylogs are insufficient for the evaluation of terms in the beta-function of $\\phi^4$ theory. Here, modular forms appear as obstructions to polylogarithmic evaluation.

David Broadhurst; Oliver Schnetz

2014-09-19

438

Two Applications of Berry's Phase in Fermionic Field Theory

When quantized fermions are coupled to a background field, nontrivial effects may arise due to the geometry and\\/or topology of the space of background field configurations. In this thesis, two examples of Berry's geometrical phase in a fermionic sea are studied: the anomalous commutator in gauge field theory and the intrinsic orbital angular momentum in superfluid ^3He-A. Chapter 1 is

William Eugene Goff

1989-01-01

439

Relating the archetypes of logarithmic conformal field theory

NASA Astrophysics Data System (ADS)

Logarithmic conformal field theory is a rich and vibrant area of modern mathematical physics with well-known applications to both condensed matter theory and string theory. Our limited understanding of these theories is based upon detailed studies of various examples that one may regard as archetypal. These include the c=-2 triplet model, the Wess-Zumino-Witten model on SL(2;R) at level k=-1/2 >, and its supergroup analogue on GL(1|1). Here, the latter model is studied algebraically through representation theory, fusion and modular invariance, facilitating a subsequent investigation of its cosets and extended algebras. The results show that the archetypes of logarithmic conformal field theory are in fact all very closely related, as are many other examples including, in particular, the SL(2|1) models at levels 1 and -1/2 >. The conclusion is then that the archetypal examples of logarithmic conformal field theory are practically all the same, so we should not expect that their features are in any way generic. Further archetypal examples must be sought.

Creutzig, Thomas; Ridout, David

2013-07-01

440

Modeling pollutant transport using a meshless-lagrangian particle model

A combined meshless-Lagrangian particle transport model is used to predict pollutant transport over irregular terrain. The numerical model for initializing the velocity field is based on a meshless approach utilizing multiquadrics established by Kansa. The Lagrangian particle transport technique uses a random walk procedure to depict the advection and dispersion of pollutants over any type of surface, including street and city canyons

Carrington, D. B. (David B.); Pepper, D. W. (Darrell W.)

2002-01-01

441

String field theory solution for any open string background

NASA Astrophysics Data System (ADS)

We present an exact solution of open bosonic string field theory which can be used to describe any time-independent open string background. The solution generalizes an earlier construction of Kiermaier, Okawa, and Soler, and assumes the existence of boundary condition changing operators with nonsingular OPEs and vanishing conformal dimension. Our main observation is that boundary condition changing operators of this kind can describe nearly any open string background provided the background shift is accompanied by a timelike Wilson line of sufficient strength. As an application we analyze the tachyon lump describing the formation of a D$(p-1)$-brane in the string field theory of a D$p$-brane, for generic compactification radius. This not only provides a proof of Sen's second conjecture, but also gives explicit examples of higher energy solutions, confirming analytically that string field theory can "reverse" the direction of the worldsheet RG flow. We also find multiple D-brane solutions, demonstrating that string field theory can add Chan-Paton factors and change the rank of the gauge group. Finally, we show how the solution provides a remarkably simple and nonperturbative proof of the background independence of open bosonic string field theory.

Erler, Theodore; Maccaferri, Carlo

2014-10-01

442

String Field Theory Solution for Any Open String Background

We present an exact solution of open bosonic string field theory which can be used to describe any time-independent open string background. The solution generalizes an earlier construction of Kiermaier, Okawa, and Soler, and assumes the existence of boundary condition changing operators with nonsingular OPEs and vanishing conformal dimension. Our main observation is that boundary condition changing operators of this kind can describe nearly any open string background provided the background shift is accompanied by a timelike Wilson line of sufficient strength. As an application we analyze the tachyon lump describing the formation of a D$(p-1)$-brane in the string field theory of a D$p$-brane, for generic compactification radius. This not only provides a proof of Sen's second conjecture, but also gives explicit examples of higher energy solutions, confirming analytically that string field theory can "reverse" the direction of the worldsheet RG flow. We also find multiple D-brane solutions, demonstrating that string field theory can add Chan-Paton factors and change the rank of the gauge group. Finally, we show how the solution provides a remarkably simple and nonperturbative proof of the background independence of open bosonic string field theory.

Theodore Erler; Carlo Maccaferri

2014-10-04

443

NASA Astrophysics Data System (ADS)

We consider perturbations of a static and spherically symmetric background endowed with a metric tensor and a scalar field in the framework of the effective field theory of modified gravity. We employ the previously developed 2 +1 +1 canonical formalism of a double Arnowitt-Deser-Misner (ADM) decomposition of space-time, which singles out both time and radial directions. Our building block is a general gravitational action that depends on scalar quantities constructed from the 2 +1 +1 canonical variables and the lapse. Variation of the action up to first order in perturbations gives rise to three independent background equations of motion, as expected from spherical symmetry. The dynamical equations of linear perturbations follow from the second-order Lagrangian after a suitable gauge fixing. We derive conditions for the avoidance of ghosts and Laplacian instabilities for the odd-type perturbations. We show that our results not only incorporate those derived in the most general scalar-tensor theories with second-order equations of motion (the Horndeski theories) but they can be applied to more generic theories beyond Horndeski.

Kase, Ryotaro; Gergely, László Á.; Tsujikawa, Shinji

2014-12-01

444

We argue that generic nonrelativistic quantum field theories with a holographic description are dual to Ho?ava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a nonrelativistic scaling limit. PMID:23473127

Janiszewski, Stefan; Karch, Andreas

2013-02-22

445

Kepler's Law in Relativistic Field Theories

NASA Astrophysics Data System (ADS)

An important current problem in gravitational physics is that of modeling the orbits of binary systems. Among such systems, those comprising a pair of black holes are particularly important due to the relative strength of the gravitational radiation they produce. As a result, many clever techniques are being invented to generate initial data sets for general relativity describing binary black holes. However, it may not be entirely clear which of these data sets are physical. In Newtonian theory, Kepler's law ties together the basic orbital parameters --- the masses, separation and velocities of the two objects --- by demanding dynamical stability of the orbit itself. However, a similar analysis in general relativity would be considerably more subtle. This presentation investigates how one might derive a modified version of Kepler's law which applies to binary black hole systems in full, non-linear general relativity. This investigation is conducted using a much- simplified toy model, and possible pitfalls in extending its results to general relativity will be discussed.

Beetle, Christopher

2005-04-01

446

NASA Technical Reports Server (NTRS)

A 3-D finite element program capable of simulating the dynamic behavior in the vicinity of the impact point, together with predicting the dynamic response in the remaining part of the structural component subjected to high velocity impact is discussed. The finite algorithm is formulated in a general moving coordinate system. In the vicinity of the impact point contained by a moving failure front, the relative velocity of the coordinate system will approach the material particle velocity. The dynamic behavior inside the region is described by Eulerian formulation based on a hydroelasto-viscoplastic model. The failure front which can be regarded as the boundary of the impact zone is described by a transition layer. The layer changes the representation from the Eulerian mode to the Lagrangian mode outside the failure front by varying the relative velocity of the coordinate system to zero. The dynamic response in the remaining part of the structure described by the Lagrangian formulation is treated using advanced structural analysis. An interfacing algorithm for coupling CELFE with NASTRAN is constructed to provide computational capabilities for large structures.

Lee, C. H.

1978-01-01

447

A scalar-tensor theory and the new interaction

NASA Astrophysics Data System (ADS)

A scalar-tensor theory is discussed whose weak field limit reproduces the potential of Fischbach et al. (1986). Three parameters in the theory are directly related to thhe three experimental constants, G(inf), alpha, and lambda. The present theory belongs to a family of scalar-tensor theories obtainable from a five-dimensional Lagrangian, and the coupling between the scalar and tensor fields, given as a consequence of the projection to four dimensions, produces the scalar tensor field.

Pimentel, Luis O.; Obregon, Octavio

1986-10-01

448

Sep 14, 2004 ... In sections 3 and 4 we apply the semi-Lagrangian relaxation to the p-median problem. In section 5 we ...... an interpreted language (although our oracles are coded in C). ..... www.cs.wisc.edu/?musicant/data/cplex/. Reinelt ...

2004-09-15

449

Comments on nonunitary conformal field theories

As is well-known, nonunitary RCFTs are distinguished from unitary ones in a number of ways, two of which are that the vacuum 0 doesn't have minimal conformal weight, and that the vacuum column of the modular S matrix isn't positive. However there is another primary field, call it o, which has minimal weight and has positive S column. We find that often there is a precise and useful relationship, which we call the Galois shuffle, between primary o and the vacuum; among other things this can explain why (like the vacuum) its multiplicity in the full RCFT should be 1. As examples we consider the minimal WSU(N) models. We conclude with some comments on fractional level admissible representations of affine algebras. As an immediate consequence of our analysis, we get the classification of an infinite family of nonunitary WSU(3) minimal models in the bulk.

T. Gannon

2003-05-08

450

Localization and diffusion in polymer quantum field theory

NASA Astrophysics Data System (ADS)

Polymer quantization is a nonstandard approach to quantizing a classical system inspired by background-independent approaches to quantum gravity such as loop quantum gravity. When applied to field theory it introduces a characteristic polymer scale at the level of the fields' classical configuration space. Compared with models with space-time discreteness or noncommutativity, this is an alternative way in which a characteristic scale can be introduced in a field theoretic context. Motivated by this comparison we study here localization and diffusion properties associated with polymer field observables and dispersion relation in order to shed some light on the novel physical features introduced by polymer quantization. While localization processes seems to be only mildly affected by polymer effects, we find that polymer diffusion differs significantly from the "dimensional reduction" picture emerging in other Planck-scale models beyond local quantum field theory.

Arzano, Michele; Letizia, Marco

2014-11-01

451

A theory is developed to describe quantitatively the idea that in an ionized gas subject to an imposed magnetic field, such as the ionosphere, the lines of magnetic flux are approximately equipotential lines. The ionosphere is assumed to be horizontally stratified, and the case in which the earth's magnetic field is vertical is considered. Small-scale electro- static fields are studied

1959-01-01

452

Quantum field theories on algebraic curves. I. Additive bosons

NASA Astrophysics Data System (ADS)

Using Serre's adelic interpretation of cohomology, we develop a `differential and integral calculus' on an algebraic curve X over an algebraically closed field k of constants of characteristic zero, define algebraic analogues of additive multi-valued functions on X and prove the corresponding generalized residue theorem. Using the representation theory of the global Heisenberg algebra and lattice Lie algebra, we formulate quantum field theories of additive and charged bosons on an algebraic curve X. These theories are naturally connected with the algebraic de Rham theorem. We prove that an extension of global symmetries (Witten's additive Ward identities) from the k-vector space of rational functions on X to the vector space of additive multi-valued functions uniquely determines these quantum theories of additive and charged bosons.

Takhtajan, Leon A.

2013-04-01

453

Torsion waves in metric-affine field theory

The approach of metric-affine field theory is to define spacetime as a real oriented 4-manifold equipped with a metric and an affine connection. The 10 independent components of the metric tensor and the 64 connection coefficients are the unknowns of the theory. We write the Yang-Mills action for the affine connection and vary it both with respect to the metric

Alastair D. King; Dmitri Vassiliev

2001-01-01

454

Nonrelativistic noncommutative field theory and UV-IR mixing

We study a non-commutative non-relativistic scalar field theory in 2+1 dimensions. The theory shows the UV-IR mixing typical of QFT on non-commutative spaces. The one-loop correction to the two-point function turns out to be given by a delta function in momentum space. The one-loop correction to the four-point function is of logarithmic type. We also evaluate the thermodynamic potential at

Joaquim Gomis; Karl Landsteiner; Esperanza Lopez

2000-01-01

455

Large Field Inflations from Higher Dimensional Gauge Theories

Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model appears as the most promising model in this framework.

Furuuchi, Kazuyuki

2014-01-01

456

Large Field Inflations from Higher Dimensional Gauge Theories

Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model appears as the most promising model in this framework.

Kazuyuki Furuuchi; Yoji Koyama

2014-07-15

457

Infrared and ultraviolet cutoffs of quantum field theory

NASA Astrophysics Data System (ADS)

Quantum gravity arguments and the entropy bound for effective field theories proposed by Cohen, Kaplan, and Nelson [Phys. Rev. Lett. 82, 4971 (1999)] lead us to consider two correlated scales which parametrize departures from relativistic quantum field theory at low and high energies. A simple estimate of their possible phenomenological implications leads us to identify a scale of around 100 TeV as an upper limit on the domain of validity of a quantum-field-theory description of nature. This fact agrees with recent theoretical developments in large extra dimensions. Phenomenological consequences in the beta-decay spectrum and cosmic-ray physics associated with possible Lorentz invariance violations induced by the infrared scale are discussed. It is also suggested that this scale might produce new unexpected effects at the quantum level.

Carmona, J. M.; Cortés, J. L.

2002-01-01

458

Noncausal propagation in spin-0 theories with external field interactions

NASA Technical Reports Server (NTRS)

The two-component Sakata-Taketani (ST) spin-0 theory and the single-component Klein-Gordon theory are obtained from the five-component Duffin-Kemmer-Petiau (DKP) theory with six types of external field interactions by means of a Peirce decomposition. Whereas the DKP equation manifests the covariance, the ST equation manifests the causal properties. In particular, the presence of noncausal wave propagation when there is coupling to a second-rank tensor field is apparent from the form of the ST equation, in which the coefficients of all the space derivatives depend on the external field. The results indicate that the causal properties of higher-spin equations should also be obvious when they are expressed in 2(2J + 1)-component Schroedinger form

Guertin, R. F.; Wilson, T. L.

1977-01-01

459

Quantum entanglement of local operators in conformal field theories.

We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles. PMID:24702348

Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi

2014-03-21

460

Scaling behavior of three-dimensional group field theory

NASA Astrophysics Data System (ADS)

Group field theory is a generalization of matrix models, with triangulated pseudomanifolds as Feynman diagrams and state sum invariants as Feynman amplitudes. In this paper, we consider Boulatov's three-dimensional model and its Freidel-Louapre positive regularization (hereafter the BFL model) with an 'ultraviolet' cutoff, and study rigorously their scaling behavior in the large cutoff limit. We prove an optimal bound on large order Feynman amplitudes, which shows that the BFL model is perturbatively more divergent than the former. We then upgrade this result to the constructive level, using, in a self-contained way, the modern tools of constructive field theory: we construct the Borel sum of the BFL perturbative series via a convergent 'cactus' expansion, and establish the 'ultraviolet' scaling of its Borel radius. Our method shows how the 'sum over triangulations' in quantum gravity can be tamed rigorously, and paves the way for the renormalization program in group field theory.

Magnen, Jacques; Noui, Karim; Rivasseau, Vincent; Smerlak, Matteo

2009-09-01