Journal of Research of the National Bureau of Standards
Maxwell's equations can be interpreted as two conservation laws in a four-dimensional geometric manifold, expressed as the vanishing of a divergence and of a curl. These natural derivatives are invariant under holonomic coordinate transformations in any geometric manifold, and contain no reference to properties of the manifold such as its metric tensor and linear connection. The relation between the D-H and E-B fields is classically determined by the metric tensor. If a general asymmetric connection is considered, the field relations can still be derived from Hamilton's principle with the addition of an anholonomic constraint. The basic effect of the inclusion of asymmetry (a non-vanishing torsion) is to destroy the parallelism between the Poynting vector E X H and the momentum vector D X B.
J. Res. Nat. Bur. Stand. Sec. B: Math. Sci., Vol. 81B, No. 1-2, p. 1
1 and 2
ABBYY FineReader 8.0
The Journal of Research of the National Institute of Standards and Technology is a publication of the U.S. Government. The papers are in the public domain and are not subject to copyright in the United States. However, please pay special attention to the