Semi- and Non-Relativistic Limit of the Dirac Dynamics with External Fields

Martin L.R. Fürst, Max Lein

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1 Citation (Scopus)

Abstract

We show how to approximate Dirac dynamics for electronic initial states by semi- and non-relativistic dynamics. To leading order, these are generated by the semi- and non-relativistic Pauli hamiltonian where the kinetic energy is related to √ m2 ξ2 and 1/2m ξ2, respectively. Higher-order corrections can in principle be computed to any order in the small parameter υ/c which is the ratio of typical speeds to the speed of light. Our results imply the dynamics for electronic and positronic states decouple to any order in υ/c ≪. To decide whether to get semi- or non-relativistic effective dynamics, one needs to choose a scaling for the kinetic momentum operator. Then the effective dynamics are derived using space-adiabatic perturbation theory by Panati et al. (Adv Theor Math Phys 7:145-204, 2003) with the novel input of a magnetic pseudodifferential calculus adapted to either the semi- or non-relativistic scaling.

Original languageEnglish
Pages (from-to)1305-1347
Number of pages43
JournalAnnales Henri Poincare
Volume14
Issue number5
DOIs
Publication statusPublished - 2013 Jul
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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