Symmetry operators and separation of variables in the (2 + 1)-dimensional Dirac equation with external electromagnetic field

A. V. Shapovalov, A. I. Breev

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We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a (2 + 1)-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a (2 + 1)-dimensional Minkowski (flat) space. For each of the sets, we carry out a complete separation of variables in the Dirac equation and find a corresponding electromagnetic potential permitting separation of variables.

Original languageEnglish
Article number1850085
JournalInternational Journal of Geometric Methods in Modern Physics
Issue number5
Publication statusPublished - 1 May 2018



  • (2 + 1)-dimensional Dirac equation
  • separation of variables
  • symmetry operators

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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