Baekler, Peter and Favaro, Alberto and Itin, Yakov and Hehl, Friedrich (2014) The Kummer tensor density in electrodynamics and in gravity. Annals of Physics, 349. pp. 297-324. ISSN 0003-4916

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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∼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 R_ijkl of a Riemann–Cartan spacetime, then K∼R^3 and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K 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).

Item Type: Article
Uncontrolled Keywords: Kummer tensor; Premetric electrodynamics; Fresnel surface; General relativity; Poincaré gauge theory; Principal null directions
Subjects: Science and mathematics > Physics
Divisions: Faculty of Mathematics and Science > Institute of Physics (IfP)
Date Deposited: 19 Mar 2015 11:14
Last Modified: 19 Mar 2015 11:14
URN: urn:nbn:de:gbv:715-oops-22763
DOI: doi:10.1016/j.aop.2014.06.007

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