Semi-relativistic approximations of the Dirac equation : First and second order corrections

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Abstract

We deal with the Dirac equation with time-dependent, non-homogeneous electro-magnetic potential, in particular with its approximation in the limit of infinite speed of light. For the linear case (given potential) we present a rigorous derivation of approximations in first and second order in the small parameter e = 1/c. Our method is based on the use of appropriate projection operators for the electron and the positron component of the spinor which are better suited than the simple splitting into "upper (large)" and "lower (small) component". We also discuss the question of a self-consistent modeling of the Pauli equation as the O(e) approximation. We suggest a coupling to an equation which is an "electro-magneto-static" O(e) approximation of the Maxwell equations consisting of Poisson equations for the four components of the potential.
Original languageEnglish
Pages (from-to)449-464
Number of pages16
JournalTransport Theory and Statistical Physics
Volume29
Issue number3-5
Publication statusPublished - 2000

Austrian Fields of Science 2012

  • 1010 Mathematics

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