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26 April 2024 |
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Relativistic covariance of Ohm's law | | R. Starke
; G. A. H. Schober
; | | Date: |
12 Sep 2014 | | Abstract: | The derivation of relativistic generalizations of Ohm’s law has been a
long-term issue in theoretical physics with deep implications for the study of
relativistic plasmas in astrophysics and cosmology. Here we propose an
alternative route to this problem by introducing the most general Lorentz
covariant first order response law, which is written in terms of the
fundamental response tensor $chi^mu_{~
u}$ relating induced four-currents to
external four-potentials. We show the equivalence of this description to Ohm’s
law and thereby prove the validity of Ohm’s law in every frame of reference. We
further use the universal relation between $chi^mu_{~
u}$ and the
microscopic conductivity tensor $sigma_{kell}$ to derive a fully relativistic
transformation law for the latter, which includes all effects of anisotropy and
relativistic retardation. In the special case of a constant, scalar
conductivity this transformation law reproduces a standard textbook
generalization of Ohm’s law. | | Source: | arXiv, 1409.3723 | | Services: | Forum | Review | PDF | Favorites | |
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