Linear media in classical electrodynamics and the Post constraint

Abstract

The Maxwell equations are formulated in a generally covariant and metric-free way in 1+3 and subsequently in 4 dimensions. For this purpose, we use the excitations $\mathcal{D}$, $\mathcal{H}$ and the field strengths $E,B$. A local and linear constitutive law between excitations and field strengths is assumed, with a constitutive tensor ${\chi }^{ijkl}=-{\chi }^{jikl}=-{\chi }^{ijlk}$ of 36 components. The properties of this tensor are discussed. In particular, we address the validity of the Post constraint, a subject that is very much under discussion. In this connection, the Tellegen gyrator, the axion field, and the ``perfect electromagnetic conductor'' of Lindell & Sihvola are compared with each other.

15 pages, latex

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• Non-minimal coupling of photons and axions
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• On Kottler's path: origin and evolution of the premetric program in gravity and in electrodynamics
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• Non-minimal Einstein-Maxwell theory: the Fresnel equation and the Petrov classification of a trace-free susceptibility tensor
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• Axiomatics of classical electrodynamics and its relation to gauge field theory
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• New Perspectives On the Relevance of Gravitation for the Covariant Description of Electromagnetically Polarizable Media
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