Maxwell's equations in Minkowski's world: their premetric generalization and the electromagnetic energy-momentum tensor
arXiv:0807.4249 · doi:10.1002/andp.200810320
Abstract
In December 1907, Minkowski expressed the Maxwell equations in the very beautiful and compact 4-dimensional form: lor f=-s, lor F^*=0. Here `lor', an abbreviation of Lorentz, represents the 4-dimensional differential operator. We study Minkowski's derivation and show how these equations generalize to their modern premetric form in the framework of tensor and exterior calculus (valid also in general relativity). After mentioning some applications of premetric electrodynamics, we turn to Minkowski's discovery of the energy-momentum tensor of the electromagnetic field. We discuss how he arrived at it and how its premetric formulation looks like.
14 pages latex in AdP-style, to appear in the special (Sept/Oct 2008) issue of Annalen der Physik (Berlin) commemorating H. Minkowski's 1908 lecture in Cologne
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