Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Kummer tensor density in electrodynamics and in gravity   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, ${\cal K}^{ijkl}$. This tensor density is, by
definition, a cubic algebraic functional of a tensor density of rank four
${\cal T}^{ijkl}$, which is antisymmetric in its first two and its last two
indices: ${\cal T}^{ijkl} = - {\cal T}^{jikl} = - {\cal T}^{ijlk}$. Thus,
${\cal K}\sim {\cal T}^3$, see Eq.(46). (i) If $\cal T$ is identified with the
electromagnetic response tensor of local and linear media, the Kummer tensor
density encompasses the generalized {\it Fresnel wave surfaces} for propagating
light. In the reversible case, the wave surfaces turn out to be {\it Kummer
surfaces} as defined in algebraic geometry (Bateman 1910). (ii) If $\cal T$ is
identified with the {\it curvature} tensor $R^{ijkl}$ of a Riemann-Cartan
spacetime, then ${\cal K}\sim R^3$ and, in the special case of general
relativity, ${\cal K}$ reduces to the Kummer tensor of Zund (1969). This $\cal
K$ is related to the {\it principal null directions} of the curvature. We
discuss the properties of the general Kummer tensor density. In particular, we
decompose $\cal K$ irreducibly under the 4-dimensional linear group $GL(4,R)$
and, subsequently, under the Lorentz group $SO(1,3)$.

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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: math
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: adap-org