Baekler, Peter, Favaro, Alberto, Itin, Yakov and Hehl, Friedrich W. ORCID: 0000-0003-2503-4744 (2014). The Kummer tensor density in electrodynamics and in gravity. Ann. Phys., 349. S. 297 - 325. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1096-035X
Full text not available from this repository.Abstract
Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K-ijkl. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T-ijkl. which is antisymmetric in its first two and its last two indices: T-ijkl = -T-jikl= -T-ijlk. Thus K similar to T-3, see Eq. (46). (i) If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor Rum of a Riemann-Cartan spacetime, then K similar to R-3 and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This X is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4, R) and, subsequently, under the Lorentz group SO(1, 3). (C) 2014 Elsevier Inc. All rights reserved.
Item Type: | Journal Article | ||||||||||||||||||||
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URN: | urn:nbn:de:hbz:38-428333 | ||||||||||||||||||||
DOI: | 10.1016/j.aop.2014.06.007 | ||||||||||||||||||||
Journal or Publication Title: | Ann. Phys. | ||||||||||||||||||||
Volume: | 349 | ||||||||||||||||||||
Page Range: | S. 297 - 325 | ||||||||||||||||||||
Date: | 2014 | ||||||||||||||||||||
Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | ||||||||||||||||||||
Place of Publication: | SAN DIEGO | ||||||||||||||||||||
ISSN: | 1096-035X | ||||||||||||||||||||
Language: | English | ||||||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||||||
Subjects: | no entry | ||||||||||||||||||||
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URI: | http://kups.ub.uni-koeln.de/id/eprint/42833 |
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