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Speaker |
Itin, Yakov |
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Coauthors |
Baekler, Peter; Favaro,Alberto; Hehl, Friedrich W. |
| Talk Title |
The Kummer Tensor Density In Electrodynamics And In Gravity. |
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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, Kijkl. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four Tijkl, which is antisymmetric in its first two and its last two indices: Tijkl=−Tjikl=−Tijlk. Thus, K∼T3. (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. (ii) If T is identified with the curvature tensor Rijkl of a Riemann–Cartan spacetime, then K∼R3 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). Published in Annals of Physics, 349, 297-324 (2014). |
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