Maxwell's equations in Minkowski's world: their premetric generalization and the electromagnetic energy-momentum tensor
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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.
Ann. Phys. (Berlin) 17, No. 9 - 10, 691 - 704 (2008) / DOI 10.1002/andp.200810320