Details
| Original language | English |
|---|---|
| Article number | 1850182 |
| Journal | International Journal of Geometric Methods in Modern Physics |
| Volume | 15 |
| Issue number | supp01 |
| Publication status | Published - 20 Aug 2018 |
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 (SR) 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 spacetime 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 spacetimes with significantly less symmetries. This result, which seems to be new, not only generalizes 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.
Keywords
- Energy-momentum tensor, Laue's theorem, momentum map
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: International Journal of Geometric Methods in Modern Physics, Vol. 15, No. supp01, 1850182, 20.08.2018.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Laue's theorem revisited
T2 - Energy-momentum tensors, symmetries, and the habitat of globally conserved quantities
AU - Giulini, Domenico
N1 - Publisher Copyright: © 2018 World Scientific Publishing Company. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/8/20
Y1 - 2018/8/20
N2 - 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 (SR) 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 spacetime 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 spacetimes with significantly less symmetries. This result, which seems to be new, not only generalizes 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.
AB - 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 (SR) 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 spacetime 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 spacetimes with significantly less symmetries. This result, which seems to be new, not only generalizes 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.
KW - Energy-momentum tensor
KW - Laue's theorem
KW - momentum map
UR - http://www.scopus.com/inward/record.url?scp=85052740823&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1808.09320
DO - 10.48550/arXiv.1808.09320
M3 - Article
AN - SCOPUS:85052740823
VL - 15
JO - International Journal of Geometric Methods in Modern Physics
JF - International Journal of Geometric Methods in Modern Physics
SN - 0219-8878
IS - supp01
M1 - 1850182
ER -