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TMF, 2018, Volume 197, Number 2, Pages 208–229 (Mi tmf9514)  

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

DOI: https://doi.org/10.4213/tmf9514

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

Bibliographic databases:

Document Type: Article
Received: 21.11.2017
Revised: 15.02.2018

Citation: V. N. Shapovalov, “Symmetry and classification of the Dirac–Fock equation”, TMF, 197:2 (2018), 208–229; Theoret. and Math. Phys., 197:2 (2018), 1572–1591

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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