Relativistic Remnants of Non-Relativistic Electrons

Taro Kashiwa; Taisuke Yamaguchi

doi:10.1093/ptep/ptu126

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arXiv · 1502.07653

Relativistic Remnants of Non-Relativistic Electrons

Taro Kashiwa·Taisuke Yamaguchi

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Abstract

Electrons obeying the Dirac equation are investigated under the non-relativistic $c \mapsto \infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.

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Taro Kashiwa, Taisuke Yamaguchi. 2014-10-09. Relativistic Remnants of Non-Relativistic Electrons. https://doi.org/10.1093/ptep/ptu126

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