Continuity equations for bound electromagnetic field and the electromagnetic energy–momentum tensor

In the framework of the teleparallel equivalent of general relativity, we study the dynamics of a gravitationally coupled electromagnetic field. It is shown that the electromagnetic field is able not only to couple to torsion, but also, through its energy–momentum tensor, produce torsion. Furthermore, it is shown that the coupling of the electromagnetic field with torsion preserves the local gauge invariance of Maxwell's theory.

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PROOF OF THE UNIQUENESS OF THE ENERGY MOMENTUM TENSOR OF THE ELECTROMAGNETIC FIELD

The Theory of Space, Time and Gravitation ◽

10.1016/b978-0-08-010061-6.50017-2 ◽

1964 ◽

pp. 411-416

Keyword(s):

Electromagnetic Field ◽

Energy Momentum Tensor ◽

Momentum Tensor

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The Maxwell equations

10.1093/oso/9780198786399.003.0030 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Electromagnetic Field ◽

Angular Momentum ◽

Variational Principle ◽

Maxwell Equations ◽

Energy Momentum Tensor ◽

Momentum Tensor ◽

Field Energy ◽

Total Charge ◽

Faraday’S Law ◽

System Energy

This chapter presents Maxwell equations determining the electromagnetic field created by an ensemble of charges. It also derives these equations from the variational principle. The chapter studies the equation’s invariances: gauge invariance and invariance under Poincaré transformations. These allow us to derive the conservation laws for the total charge of the system and also for the system energy, momentum, and angular momentum. To begin, the chapter introduces the first group of Maxwell equations: Gauss’s law of magnetism, and Faraday’s law of induction. It then discusses current and charge conservation, a second set of Maxwell equations, and finally the field–energy momentum tensor.

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Further comments on the equivalence of Abraham's, Minkowski's, and others' electrodynamics

Canadian Journal of Physics ◽

10.1139/p80-155 ◽

1980 ◽

Vol 58 (8) ◽

pp. 1163-1170 ◽

Cited By ~ 15

Author(s):

Gérard A. Maugin

Keyword(s):

Energy Density ◽

Total Energy ◽

Mechanical Behavior ◽

Internal Energy ◽

Closed System ◽

Ad Hoc ◽

Energy Momentum Tensor ◽

Momentum Tensor ◽

Electromagnetic Energy ◽

Time Decomposition

Arguments recently proposed by Kranyš concerning the nondistinguishability between Abraham's and Minkowski's electromagnetic contributions to the total energy-momentum tensor of the same relativistic, thermodynamically closed system are extended to other electromagnetic energy-momentum tensors (as proposed by Grot and Eringen and de Groot and Suttorp). The adjustment of the corresponding "matter" contribution, which occurs in each element of the canonical space-time decomposition of the total energy-momentum tensor, is exhibited in those different cases. For dissipation-free systems this adjustment can be achieved for each case by means of an ad hoc Legendre transformation on the internal energy density. The arguments used do not presuppose any isotropy and linearity of the medium and can be readily extended to the cases of media with hysteresis and media endowed with intrinsic spins, be they of a fluid-like or solid-like type of mechanical behavior.

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