scholarly journals Symmetries and Covariant Poisson Brackets on Presymplectic Manifolds

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 70
Author(s):  
Florio M. Ciaglia ◽  
Fabio Di Cosmo ◽  
Alberto Ibort ◽  
Giuseppe Marmo ◽  
Luca Schiavone ◽  
...  
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Embedding Theorem ◽  
Tensor Algebra ◽  
Poisson Brackets ◽  
Momentum Map ◽  
First Order ◽  
Klein Gordon ◽  
Presymplectic Structure ◽  
Conserved Currents

As the space of solutions of the first-order Hamiltonian field theory has a presymplectic structure, we describe a class of conserved charges associated with the momentum map, determined by a symmetry group of transformations. A gauge theory is dealt with by using a symplectic regularization based on an application of Gotay’s coisotropic embedding theorem. An analysis of electrodynamics and of the Klein–Gordon theory illustrate the main results of the theory as well as the emergence of the energy–momentum tensor algebra of conserved currents.

Conserved currents of the Klein–Gordon field

1981 ◽  
Vol 90 (3) ◽  
pp. 507-515 ◽  
Author(s):  
T. J. Gordon
Keyword(s):  
Field Theory ◽  
Energy Momentum Tensor ◽  
Differential Forms ◽  
Momentum Tensor ◽  
Mathematical Background ◽  
Poincaré Lemma ◽  
Klein Gordon ◽  
Countably Infinite ◽  
Infinite Set ◽  
Conserved Currents

AbstractA method is presented whereby all locally defined conserved currents of the Klein-Gordon field are found. The mathematical background to the method includes a generalization of the Poincaré lemma of the calculus of exterior differential forms. It is found that the only conserved currents are essentially a countably infinite set of functions, bilinear in the field, together with a single current in the case where the mass is zero. The usual energy-momentum tensor is included amongst these functions. The method does not depend on the use of any canonical formulation of the field theory.

scholarly journals ON SUPERLUMINAL FERMIONS WITHIN THE SECOND DERIVATIVE EQUATION

2012 ◽  
Vol 27 (14) ◽  
pp. 1250081 ◽  
Author(s):  
S. I. KRUGLOV
Keyword(s):  
Energy Momentum Tensor ◽  
Canonical Quantization ◽  
Vacuum Expectation ◽  
Momentum Tensor ◽  
Order Equation ◽  
Quantum Mechanical ◽  
Projection Operators ◽  
The Novel ◽  
First Order ◽  
Electromagnetic Interactions

We postulate the second-order derivative equation with four parameters for spin-1/2 fermions possessing two mass states. For some choice of parameters fermions propagate with the superluminal speed. Thus, the novel tachyonic equation is suggested. The relativistic 20-component first-order wave equation is formulated and projection operators extracting states with definite energy and spin projections are obtained. The Lagrangian formulation of the first-order equation is presented and the electric current and energy–momentum tensor are found. The minimal and nonminimal electromagnetic interactions of fermions are considered and Schrödinger's form of the equation and the quantum-mechanical Hamiltonian are obtained. The canonical quantization of the field in the first-order formalism is performed and we find the vacuum expectation of chronological pairing of operators.

scholarly journals Klein Gordon Field in FLRW Space-Time

2020 ◽  
Vol 13 (13) ◽  
pp. 1-4
Author(s):  
S.K. Sharma ◽  
P.R. Dhungel ◽  
U. Khanal
Keyword(s):  
Spherical Harmonics ◽  
Energy Momentum Tensor ◽  
Equation Of Motion ◽  
Momentum Tensor ◽  
Space Time ◽  
Wkb Approximation ◽  
Temporal Parts ◽  
Klein Gordon ◽  
Current Energy ◽  
Particle Current

As a continuation of solving the equations governing the perturbation of the Friedmann-Lemaitre-Robertson- Walker (FLRW) space-time in Newman-Penrose formalism, the behaviour of the massive Klein-Gordon (KG) field coupled to the FLRW has been investigated. The Equation of Motion has been written and solved separately for radial and temporal parts. The former solution has come to be in terms of the Gegenbauer polynomials and spherical harmonics and the latter being in the WKB approximation. The particle current, energy momentum tensor and potential have also been obtained.

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.

Scale invariance and the energy–momentum tensor

1970 ◽  
Vol 48 (20) ◽  
pp. 2371-2375
Author(s):  
Peter Bendix
Keyword(s):  
Gravitational Field ◽  
Scale Invariance ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Scale Invariant ◽  
New Energy ◽  
Klein Gordon

A method is described by which an energy–momentum tensor can be constructed such that in addition to the usual properties of this tensor it acquires the property of scale invariance in the absence of masses and charges. (The new energy–momentum tensor constructed here is not the source of the gravitational field, however.) It is shown that the usual construction for the massless Klein–Gordon field yields an energy–momentum tensor which is not scale invariant, whereas using the construction described here, one finds a scale invariant energy–momentum tensor for this case.

POISSON BRACKETS IN FIELD THEORY

1959 ◽  
Vol 37 (1) ◽  
pp. 5-9 ◽  
Author(s):  
Hans Freistadt
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Close Connection ◽  
Tensor Algebra ◽  
Poisson Brackets ◽  
Dirac Fields ◽  
Klein Gordon ◽  
Covariant Field

Poisson brackets for covariant field theory are defined in such a way as to demonstrate the close connection and ready transition between the classical brackets and the corresponding commutators of quantum theory. The approach of Good is followed in general; but the questions of tensor algebra are handled differently, requiring the introduction of a family of space-like surfaces and their normals. As an illustration, the free Klein-Gordon and Dirac fields are worked out.

scholarly journals CONSERVED CURRENT FOR GENERAL TELEPARALLEL MODELS

2002 ◽  
Vol 17 (20) ◽  
pp. 2765-2765 ◽  
Author(s):  
Y. ITIN
Keyword(s):  
Field Equation ◽  
Vector Fields ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Geometrical Structures ◽  
Yang Mills ◽  
First Order ◽  
Diffeomorphism Invariance ◽  
Maxwell Field Equation ◽  
Conserved Current

The obstruction for the existence of an energy-momentum tensor for the gravitational field in GR is connected with vanishing of first order invariants in (pseudo) Riemannian geometry. This specific geometric property is not valid in alternative geometrical structures1,2. A parallelizable differentiable 4D-manifold endowed with a class of smooth coframe fields ϑa is considered. A general 3-parameter class of global Lorentz invariant teleparallel models is considered. It includes a 1-parameter subclass of models with the Schwarzschild coframe solution (generalized teleparallel equivalent of gravity) 3. By introducing the notion of a 3-parameter conjugate field strength F linear in the strength Ca = dϑa the coframe Lagrangian is rewritten in the Maxwell-Yang-Mills form L = 1/2Fa ∧ Ca. The field equation turns out to have a form d * Fa = Ta completely similar to the Maxwell field equation. By applying the Noether procedure, the source 3-form Ta is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source Ta of the coframe field is interpreted as the total conserved energy-momentum current of the coframe field and matter4. The energy-momentum tensor is defined as a map of the module of current 3-forms into the module of vector fields 5. Thus an energy-momentum tensor for the coframe is defined in a diffeomorphism invariant and a translational covariant way. The total energy-momentum current of a system is conserved. Thus a redistribution of the energy-momentum current between material and coframe (gravity) field is possible in principle, unlike as in the standard GR. The result is: The standard GR has a neighborhood of viable models with the same Schwarzschild solutions. These models however have a better Lagrangian behavior and produce an invariant energy-momentum tensor.

Thermodynamic consequences of specific modified gravity on the apparent horizon

2019 ◽  
Vol 16 (09) ◽  
pp. 1950144
Author(s):  
Abdul Jawad ◽  
Zoya Khan ◽  
Shamaila Rani
Keyword(s):  
Scalar Field ◽  
Modified Gravity ◽  
Energy Momentum Tensor ◽  
Apparent Horizon ◽  
Second Law Of Thermodynamics ◽  
Momentum Tensor ◽  
Isotropic Universe ◽  
First Order ◽  
Generalized Second Law ◽  
Thermodynamical Behavior

We discuss the thermodynamical behavior of homogeneous and isotropic universe (flat and non-flat) in the framework of [Formula: see text] gravity, where [Formula: see text] stands for Ricci scalar and [Formula: see text] signifies the trace of energy–momentum tensor of a scalar field [Formula: see text]. We follow through the first-order formalism that specifies the scalar field to the Hubble parameter which becomes [Formula: see text] By using Bekenstein–Hawking entropy, we analyze the validity of generalized second law of thermodynamics at apparent horizon for different values of [Formula: see text] and evaluate the equilibrium condition for all cases as well.

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