Energy–momentum tensors in classical field theories — A modern perspective

Voicu, Nicoleta

doi:10.1142/s0219887816400016

Cited by 7 publications

(12 citation statements)

References 12 publications

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“…coordinate changes. The arising Noether current gives rise to a notion of an energy-momentum distribution tensor of the gas on the tangent bundle, via the Gotay-Marsden procedure [31,32]. We will relate this new notion of energy-momentum to the usual definition of the energy-momentum tensor of a kinetic gas on the spacetime manifold M .…”

Section: The Kinetic Gas In the Language Of Finsler Geometrymentioning

confidence: 99%

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Relativistic kinetic gases as direct sources of gravity

2020

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We propose a new model for the description of a gravitating multi particle system, viewed as a kinetic gas. The properties of the, colliding or non-colliding, particles are encoded into a so called one-particle distribution function, which is a density on the space of allowed particle positions and velocities, i.e. on the tangent bundle of the spacetime manifold. We argue that an appropriate theory of gravity, describing the gravitational field generated by a kinetic gas, must also be modeled on the tangent bundle. The most natural mathematical framework for this task is Finsler spacetime geometry. Following this line of argumentation, we construct a coupling between the kinetic gas and a recently proposed Finsler geometric extension of general relativity. Additionally, we explicitly show how the coordinate invariance of the action of the kinetic gas leads to a novel formulation of conservation of the energy-momentum distribution of the gas on the tangent bundle.

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Section: The Kinetic Gas In the Language Of Finsler Geometrymentioning

confidence: 99%

“…Following [31,32], the middle term singles out the desired energy-momentum distribution tensor, which is defined as…”

Section: B the Action Of A Kinetic Gasmentioning

confidence: 99%

Relativistic kinetic gases as direct sources of gravity

2020

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“…Conversely, if X L ∈ X 4 (J 3 π) is a holonomic multivector field solution to the equation (38), at least on the points of a submanifold S f ֒→ J 3 π, and tangent to S f ; then there exists a unique holonomic multivector field X ∈ X 4 (W r ) which is a solution to the equation (10), at least on the points of (47)).…”

Section: Recovering the Lagrangian And Hamiltonian Formalisms 231 Lmentioning

confidence: 99%

“…(For a geometric study on the stress-energy-momentum tensors see, for instance, [16,17,23,31,47]). Then, we can write L S = L S (π 2 ) * η ∈ Ω 4 (J 2 π), with L S = L V + L m ∈ C ∞ (J 2 π).…”

Section: Previous Statementsmentioning

confidence: 99%

Multisymplectic unified formalism for Einstein-Hilbert gravity

Gaset

Román‐Roy

2018

Journal of Mathematical Physics

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We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified Lagrangian-Hamiltonian formalism is particularly interesting when it is applied to these kinds of theories, since it simplifies the treatment of them; in particular, the implementation of the constraint algorithm, the retrieval of the Lagrangian description, and the construction of the covariant Hamiltonian formalism. In order to apply this algorithm to the covariant field equations, they must be written in a suitable geometrical way, which consists of using integrable distributions, represented by multivector fields of a certain type. We apply all these tools to the Einstein-Hilbert model without and with energy-matter sources. We obtain and explain the geometrical and physical meaning of the Lagrangian constraints and we construct the multimomentum (covariant) Hamiltonian formalisms in both cases. As a consequence of the gauge freedom and the constraint algorithm, we see how this model is equivalent to a first-order regular theory, without gauge freedom. In the case of presence of energy-matter sources, we show how some relevant geometrical and physical characteristics of the theory depend on the type of source. In all the cases, we obtain explicitly multivector fields which are solutions to the gravitational field equations. Finally, a brief study of symmetries and conservation laws is done in this context.

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“…It can be argued that the natural setting for a thorough clarification of such matters is provided by the geometric formulation of Lagrangian field theory on jet spaces and, in particular, by generalizations of the Noether theorem expressed in terms of symmetries of the Poincaré-Cartan form [10,15,11,16,22,24,25,26,27,30,37,38,39,40]. In that context, a previous paper by M. Modugno and myself [6] offered a natural extension of the notion of canonical energy-tensor to the non-trivial bundle case, on the basis of an earlier suggestion by Hermann [19].…”

Section: Introductionmentioning

confidence: 99%

Overconnections and the energy-tensors of gauge and gravitational fields

Canarutto¹

2016

Journal of Geometry and Physics

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A geometric construction for obtaining a prolongation of a connection to a connection of a bundle of connections is presented. This determines a natural extension of the notion of canonical energy-tensor which suits gauge and gravitational fields, and shares the main properties of the energy-tensor of a matter field in the jet space formulation of Lagrangian field theory, in particular with regards to symmetries of the Poincaré-Cartan form. Accordingly, the joint energy-tensor for interacting matter and gauge fields turns out to be a natural geometric object, whose definition needs no auxiliary structures. Various topics related to energy-tensors, symmetries and the Einstein equations in a theory with interacting matter, gauge and gravitational fields can be viewed under a clarifying light. Finally, the symmetry determined by the "Komar superpotential" is expressed as a symmetry of the gravitational Poincaré-Cartan form.MSC 2010: 83C05, 83C40.PACS 2010: 02.40.Hw, 04.20.Fy.

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Energy–momentum tensors in classical field theories — A modern perspective

Cited by 7 publications

References 12 publications

Relativistic kinetic gases as direct sources of gravity

Relativistic kinetic gases as direct sources of gravity

Multisymplectic unified formalism for Einstein-Hilbert gravity

Overconnections and the energy-tensors of gauge and gravitational fields

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