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
Creators:
CreatorsEmailORCIDORCID Put Code
Baekler, PeterUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Favaro, AlbertoUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Itin, YakovUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Hehl, Friedrich W.UNSPECIFIEDorcid.org/0000-0003-2503-4744UNSPECIFIED
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
Uncontrolled Keywords:
KeywordsLanguage
ANISOTROPIC MEDIA; FIELD-EQUATIONS; GAUGE-THEORY; SURFACES; BREAKING; ALGEBRAMultiple languages
Physics, MultidisciplinaryMultiple languages
URI: http://kups.ub.uni-koeln.de/id/eprint/42833

Downloads

Downloads per month over past year

Altmetric

Export

Actions (login required)

View Item View Item