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Theoretical and Mathematical Physics

, Volume 197, Issue 2, pp 1572–1591 | Cite as

Symmetry and Classification of the Dirac–Fock Equation

  • V. N. ShapovalovEmail author
Article
  • 15 Downloads

Abstract

We consider the properties of the Dirac–Fock equation with differential operators of the first-order symmetry. For a relativistic particle in an electromagnetic field, we describe the covariant properties of the Dirac equation in an arbitrary Riemannian space V4 with the signature (−1,−1,−1, 1). We present a general form of the differential operator with a first-order symmetry and characterize the pair of such commuting operators. We list the spaces where the free Dirac equation admits at least one differential operator with a first-order symmetry. We perform a symmetry classification of electromagnetic field tensors and construct complete sets of symmetry operators.

Keywords

symmetry operator Riemannian space Dirac equation Dirac–Fock equation 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Gorodovikov Kalmyk State UniversityElistaRussia

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