scholarly journals Conserved laws and dynamical structure of axions coupled to photons

2021 ◽  
Author(s):  
Omar Rodríguez-Tzompantzi
Keyword(s):  
Degrees Of Freedom ◽  
Transition Amplitude ◽  
Momentum Tensor ◽  
Hamiltonian Reduction ◽  
Dynamical Structure ◽  
Gauge Transformations ◽  
Functional Measure ◽  
Dynamic Variables ◽  
Conserved Currents ◽  
Space Method

In this work, we carry out a study of the conserved quantities and dynamical structure of the four-dimensional modified axion electrodynamics theory described by the axion-photon coupling. In the first part of the analysis, we employ the covariant phase space method to construct the conserved currents and to derive the Noether charges associated with the gauge symmetry of the theory. We further derive the improved energy–momentum tensor using the Belinfante–Rosenfeld procedure, which leads us to the expressions for the energy, momentum, and energy flux densities. Thereafter, with the help of Faddeev–Jackiw’s Hamiltonian reduction formalism, we obtain the relevant fundamental brackets structure for the dynamic variables and the functional measure for determining the quantum transition amplitude. We also confirm that modified axion electrodynamics has three physical degrees of freedom per space point. Moreover, using this symplectic framework, we yield the gauge transformations and the structure of the constraints directly from the zero-modes of the corresponding pre-symplectic matrix.

scholarly journals Symplectic realization of two interacting spin-two fields in three dimensions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Omar Rodríguez-Tzompantzi
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Potential Gradient ◽  
Dynamic Structure ◽  
Three Dimensions ◽  
Dynamical Structure ◽  
Gauge Transformations ◽  
Zero Modes ◽  
New Perspective ◽  
Gauge Structure

Abstract We constructed a symplectic realization of the dynamic structure of two interacting spin-two fields in three dimensions. A significant simplification refers to the treatment of constraints: instead of performing a Hamiltonian analysis à la Dirac, we worked out a method that only uses properties of the pre-symplectic two-form matrix and its corresponding zero-modes to investigate the nature of constraints and the gauge structure of the theory. For instance, we demonstrate that the contraction of the zero-modes with the potential gradient, yields explicit expressions for the whole set of constraints on the dynamics of the theory, including the symmetrization condition and an explicit relationship between the coupling and cosmological constants. This way, we further identify the necessary conditions for the existence of a unique non-linear candidate for a partially massless theory, using only the expression for the interaction parameters of the model. In the case of gauge structure, the transformation laws for the entire set of dynamical variables are more straightforwardly derived from the structure of the remaining zero-modes; in this sense, the zero-modes must be viewed as the generators of the corresponding gauge transformations. Thereafter, we use an appropriate gauge-fixing procedure, the time gauge, to compute both the quantization brackets and the functional measure on the path integral associated with our model. Finally, we confirm that three-dimensional bi-gravity has two physical degrees of freedom per space point. With the above, we provide a new perspective for a better understanding of the dynamical structure of theories of interacting spin-two fields, which does not require the constraints to be catalogued as first- and second-class ones as in the case of Dirac’s standard method.

scholarly journals CANONICAL APPROACH TO 2D SUPERSYMMETRIC WZNW MODEL COUPLED TO SUPERGRAVITY

2002 ◽  
Vol 17 (29) ◽  
pp. 1923-1936 ◽  
Author(s):  
OLIVERA MIŠKOVIĆ ◽  
BRANISLAV SAZDOVIĆ
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Moody Algebra ◽  
Gauge Transformations ◽  
Local Gauge ◽  
Gauge Symmetries ◽  
Wznw Model ◽  
Canonical Approach ◽  
Explicit Expressions

Starting from the known representation of the Kac–Moody algebra in terms of the coordinates and momenta, we extend it to the representation of the super Kac–Moody and super Virasoro algebras. Then we use general canonical method to construct an action invariant under local gauge symmetries, where components of the super energy–momentum tensor L± and G± play the role of the diffeomorphisms and supersymmetry generators respectively. We obtain covariant extension of WZNW theory with respect to local supersymmetry as well as explicit expressions for gauge transformations.

Elements of Classical Field Theory

2021 ◽  
pp. 24-34
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Classical Field ◽  
Lagrange Equations ◽  
Lie Group Of Transformations ◽  
Infinitesimal Transformations ◽  
Conserved Currents

The purpose of this chapter is to recall the principles of Lagrangian and Hamiltonian classical mechanics. Many results are presented without detailed proofs. We obtain the Euler–Lagrange equations of motion, and show the equivalence with Hamilton’s equations. We derive Noether’s theorem and show the connection between symmetries and conservation laws. These principles are extended to a system with an infinite number of degrees of freedom, i.e. a classical field theory. The invariance under a Lie group of transformations implies the existence of conserved currents. The corresponding charges generate, through the Poisson brackets, the infinitesimal transformations of the fields as well as the Lie algebra of the group.

scholarly journals On the Hamiltonian approach: Applications to geophysical flows

1998 ◽  
Vol 5 (4) ◽  
pp. 219-240 ◽  
Author(s):  
V. Goncharov ◽  
V. Pavlov
Keyword(s):  
Degrees Of Freedom ◽  
Fluid Motion ◽  
Gauge Transformations ◽  
Motion Models ◽  
Canonical Variables ◽  
Long Time ◽  
Minimum Number ◽  
Nonlinear Gauge ◽  
Hydrodynamical System ◽  
General Method

Abstract. This paper presents developments of the Harniltonian Approach to problems of fluid dynamics, and also considers some specific applications of the general method to hydrodynamical models. Nonlinear gauge transformations are found to result in a reduction to a minimum number of degrees of freedom, i.e. the number of pairs of canonically conjugated variables used in a given hydrodynamical system. It is shown that any conservative hydrodynamic model with additional fields which are in involution may be always reduced to the canonical Hamiltonian system with three degrees of freedom only. These gauge transformations are associated with the law of helicity conservation. Constraints imposed on the corresponding Clebsch representation are determined for some particular cases, such as, for example. when fluid motions develop in the absence of helicity. For a long time the process of the introduction of canonical variables into hydrodynamics has remained more of an intuitive foresight than a logical finding. The special attention is allocated to the problem of the elaboration of the corresponding regular procedure. The Harniltonian Approach is applied to geophysical models including incompressible (3D and 2D) fluid motion models in curvilinear and lagrangian coordinates. The problems of the canonical description of the Rossby waves on a rotating sphere and of the evolution of a system consisting of N singular vortices are investigated.

Experimental and Theoretical Studies of Slow Crack Growth in Engineering Polymers

2007 ◽  
Vol 345-346 ◽  
pp. 493-496 ◽  
Author(s):  
Alexander Chudnovsky
Keyword(s):  
Degrees Of Freedom ◽  
Process Zone ◽  
Slow Crack Growth ◽  
High Stress ◽  
Momentum Tensor ◽  
Empirical Method ◽  
Original Material ◽  
Thermodynamic Forces ◽  
High Stress Level ◽  
Engineering Polymers

The process zone (PZ) that surrounds and precedes a crack is a common feature of fracture in engineering polymers. Depending on the material, the specimen geometry, the temperature, and the loading conditions various types of microdefects such as crazes, shearbands, microcracks, micro-voids, etc, constitute the process zone. The microdefects are formed in response to stress concentration, and shield the crack tip from high stress level. There is a complex crack – damage interaction, which is briefly addressed by means of a semi-empirical method. On a continuum mechanics level, the PZ appears as a domain with effective elastic properties different from that of the original material. The crack and PZ evolve as one system with multiple degrees of freedom. It is regarded as a Crack Layer (CL) in contrast with the conventional image of crack as an ideal cut. There are thermodynamic forces responsible for CL growth, which are defined as derivative of Gibbs free energy with respect to the corresponding CL “coordinates”. The thermodynamic forces can be expressed as integrals of the Energy Momentum Tensor of elasticity. Onsager type relations between CL growth rates and corresponding CL forces constitute a system of constitutive equations for CL propagation. Examples of solution of these equations, and comparison with experimental data as well as with conventional models are presented in accompanying paper.

scholarly journals TODA FIELD THEORIES ASSOCIATED WITH HYPERBOLIC KAC-MOODY ALGEBRA — PAINLEVÉ PROPERTIES AND W ALGEBRAS

1996 ◽  
Vol 11 (31) ◽  
pp. 5479-5493 ◽  
Author(s):  
REINHOLD W. GEBERT ◽  
SHUN’YA MIZOGUCHI ◽  
TAKEO INAMI
Keyword(s):  
Lie Algebras ◽  
Energy Momentum Tensor ◽  
Direct Calculation ◽  
Momentum Tensor ◽  
Field Theories ◽  
Painlevé Analysis ◽  
Painlevé Test ◽  
Moody Algebra ◽  
Simple Lie Algebras ◽  
Conserved Currents

We show that the Painlevé test is useful not only for probing (non)integrability but also for finding the values of spins of conserved currents (W currents) in Toda field theories (TFT’s). In the case of TFT’s based on simple Lie algebras the locations of resonances are shown to give precisely the spins of conserved W currents. We apply this test to TFT’s based strictly on hyperbolic Kac-Moody algebras and show that there exist no resonance other than that at n = 2, which corresponds to the energy-momentum tensor, indicating their nonintegrability. We also check by direct calculation that there are no spin-3 or -4 conserved currents for all the hyperbolic TFT’s in agreement with the result of our Painlevé analysis.

SCALE AND CONFORMAL INVARIANCE AND VARIATION OF THE METRIC

2006 ◽  
Vol 21 (17) ◽  
pp. 3641-3647 ◽  
Author(s):  
J. SADEGHI ◽  
A. TOFIGHI ◽  
A. BANIJAMALI
Keyword(s):  
Conformal Invariance ◽  
Scale Invariance ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Conserved Currents

We consider the relation between scale invariance and conformal invariance. In our analysis the variation of the metric is taken into account. By imposing some conditions on the trace of the energy–momentum tensor and on the variation of the action, we find that the scale dimensions of the fields are not affected. We also obtain the conserved currents. We find that the conditions for conformal invariance are stronger than for scale invariance.

scholarly journals ASYMPTOTIC SYMMETRY GROUPS OF LONG-RANGED GAUGE CONFIGURATIONS

1995 ◽  
Vol 10 (28) ◽  
pp. 2059-2070 ◽  
Author(s):  
DOMENICO GIULINI
Keyword(s):  
Degrees Of Freedom ◽  
General Setting ◽  
Discrete Subgroup ◽  
Rotation Group ◽  
Connected Component ◽  
Asymptotic Symmetry ◽  
Continuous Part ◽  
Spatial Infinity ◽  
Gauge Transformations ◽  
Yang Mills

We make some general remarks on long-ranged configurations in gauge or diffeomorphism invariant theories where the fields are allowed to assume some nonvanishing values at spatial infinity. In this case the Gauss constraint only eliminates those gauge degrees of freedom which lie in the connected component of asymptotically trivial gauge transformations. This implies that proper physical symmetries arise either from gauge transformations that reach to infinity or those that are asymptotically trivial but do not lie in the connected component of transformations within that class. The latter transformations form a discrete subgroup of all symmetries whose position in the ambient group has proven to have interesting implications. We explain this for the dyon configuration in the SO(3) Yang-Mills-Higgs theory, where we prove that the asymptotic symmetry group is Z|m|×ℝ where m is the monopole number. We also discuss the application of the general setting to general relativity and show that here the only implication of discrete symmetries for the continuous part is a possible extension of the rotation group SO(3) to SU(2).

2D SUPERGRAVITY WITH APPLICATIONS TO INTEGRABLE MODELS

1993 ◽  
Vol 08 (31) ◽  
pp. 2943-2954
Author(s):  
L. N. ARNAUDOV ◽  
E. M. PRODANOV ◽  
R. CH. RASHKOV
Keyword(s):  
Recent Work ◽  
Ward Identity ◽  
Degrees Of Freedom ◽  
Hamiltonian Reduction ◽  
Simons Theory ◽  
Curvature Condition ◽  
Zero Curvature ◽  
Covariant Action ◽  
Chern Simons ◽  
Chern Simons Theory

In recent work two different approaches for obtaining the covariant action of 2D quantum supergravity are developed. The first one is based on Hamiltonian reduction of flat OSP (2|1) connection in holomorphic polarization. Adding extra degrees of freedom with the help of gauging procedure, the action and the superconformal Ward identity are obtained. It is shown that super-Virasoro transformations preserve the form of the Lax connection and therefore are symmetries of the sKdV equations. In the second approach starting with Chern-Simons theory and using non-canonical polarization the zero-curvature condition entails the same results.

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