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Relativistic covariance of Ohm's law

The derivation of Lorentz-covariant generalizations of Ohm's law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an alternative route to this problem, which is motivated by...

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Hauptverfasser: Starke, Ronald (VerfasserIn) , Schober, Giulio Albert Heinrich (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 26 April 2016
In: International journal of modern physics
Year: 2016, Jahrgang: 25, Heft: 11
ISSN:1793-6594
DOI:10.1142/S0218271816400101
Online-Zugang:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1142/S0218271816400101
Verlag, lizenzpflichtig, Volltext: https://www.worldscientific.com/doi/abs/10.1142/S0218271816400101
Volltext
Verfasserangaben:R. Starke and G.A.H. Schober

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520 |a The derivation of Lorentz-covariant generalizations of Ohm's law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an alternative route to this problem, which is motivated by the tremendous progress in first-principles materials physics in general and ab initio electronic structure theory in particular. We start from the most general, Lorentz-covariant first-order response law, which is written in terms of the fundamental response tensor χμνχμν<math display="inline" overflow="scroll" altimg="eq-00001.gif"><mrow><msup><mi>χ</mi><mi>μ</mi></msup><mspace width="0.167em"></mspace><msub><mi></mi><mi>ν</mi></msub></mrow></math> relating induced four-currents to external four-potentials. By showing the equivalence of this description to Ohm's law, we prove the validity of Ohm's law in every inertial frame. We further use the universal relation between χμνχμν<math display="inline" overflow="scroll" altimg="eq-00002.gif"><mrow><msup><mi>χ</mi><mi>μ</mi></msup><mspace width="0.167em"></mspace><msub><mi></mi><mi>ν</mi></msub></mrow></math> and the microscopic conductivity tensor σkℓσkℓ<math display="inline" overflow="scroll" altimg="eq-00003.gif"><msub><mrow><mi>σ</mi></mrow><mrow><mi>k</mi><mi>ℓ</mi></mrow></msub></math> 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 can be used to rederive a standard textbook generalization of Ohm's law. 
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