This article is cited in 1 paper

Symmetry and classification of the Dirac–Fock equation

V. N. Shapovalov

Gorodovikov Kalmyk State University, Elista, Russia

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 $V_4$ 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.

Received: 21.11.2017
Revised: 15.02.2018

DOI: 10.4213/tmf9514

 English version: Theoretical and Mathematical Physics, 2018, 197:2, 1572–1591

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