A restatement of the normal form theorem for area metrics

Details A restatement of the normal form theorem for area metrics A restatement of the normal form theorem for area metrics

2011-08-21

arxiv.org/abs/1108.4198v2

Physics

Mathematical Physics

Updated proof of Proposition A.2 (Claim 5). Fixed typo in Theorem 6 (Metaclass XXIII)

Scientific paper

An area metric is a (0,4)-tensor with certain symmetries on a 4-manifold that represent a non-dissipative linear electromagnetic medium. A recent result by Schuller, Witte and Wohlfarth provides a pointwise normal form theorem for such area metrics. This result is similar to the Jordan normal form theorem for (1,1)-tensors, and the result shows that any area metric belongs to one of 23 metaclasses with explicit coordinate expressions for each metaclass. In this paper we restate and prove this result for skewon-free (2,2)-tensors and show that in general, each metaclasses has three different coordinate representations, and each of metaclasses I, II, ..., VI, VII need only one coordinate representation.

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