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