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Laue's Theorem Revisited: Energy-Momentum Tensors, Symmetries, and the Habitat of Globally Conserved Quantities

Giulini, Domenico (2018) Laue's Theorem Revisited: Energy-Momentum Tensors, Symmetries, and the Habitat of Globally Conserved Quantities. International Journal of Geometric Methods in Modern Physics, 15 (10). pp. 1850182-1.

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Abstract

The energy-momentum tensor for a particular matter component summarises its local energy-momentum distribution in terms of densities and current densities. We re-investigate under what conditions these local distributions can be integrated to meaningful global quantities. This leads us directly to a classic theorem by Max von Laue concerning integrals of components of the energy-momentum tensor, whose statement and proof we recall. In the first half of this paper we do this within the realm of Special Relativity and in the traditional mathematical language using components with respect to affine charts, thereby focusing on the intended physical content and interpretation. In the second half we show how to do all this in a proper differential-geometric fashion and on arbitrary space-time manifolds, this time focusing on the group-theoretic and geometric hypotheses underlying these results. Based on this we give a proper geometric statement and proof of Laue's theorem, which is shown to generalise from Minkowski space (which has the maximal number of isometries) to space-times with significantly less symmetries. This result, which seems to be new, not only generalises but also clarifies the geometric content and hypotheses of Laue's theorem. A series of three appendices lists our conventions and notation and summarises some of the conceptual and mathematical background needed in the main text.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Giulini, Domenico0000-0003-3123-7257
Keywords: energy-momentum tensor, momentum map, Laue’s theorem
Subjects: Specific Sciences > Physics > Classical Physics
Specific Sciences > Physics > Relativity Theory
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Domenico Giulini
Date Deposited: 29 Aug 2018 23:51
Last Modified: 29 Aug 2018 23:51
Item ID: 14986
Journal or Publication Title: International Journal of Geometric Methods in Modern Physics
Publisher: World Scientific
Official URL: https://www.worldscientific.com/worldscinet/ijgmmp
DOI or Unique Handle: https://doi.org/10.1142/S0219887818501827
Subjects: Specific Sciences > Physics > Classical Physics
Specific Sciences > Physics > Relativity Theory
Specific Sciences > Physics > Symmetries/Invariances
Date: 20 August 2018
Page Range: pp. 1850182-1
Volume: 15
Number: 10
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/14986

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