A RESTATEMENT OF THE ALGEBRAIC CLASSIFICATION OF AREA METRICS ON 4-MANIFOLDS
Matias F. Dahl · International Journal of Geometric Methods in Modern Physics · 2012
An area metric is a [Formula: see text]-tensor with certain symmetries on a 4-manifold that represents a non-dissipative linear electromagnetic medium. A recent result by Schuller, Witte and Wohlfarth gives a pointwise algebraic classification for such area metrics. This result is similar to the Jordan normal form theorem for [Formula: see text]-tensors, and the result shows that pointwise area metrics divide into 23 metaclasses and each metaclass requires two coordinate representations. For the first 7 metaclasses, we show that only one coordinate representation is needed. For the remaining 16 metaclasses we find an additional third coordinate representation.