Symmetry and Classification of the Dirac–Fock Equation

• Published in: Theoretical and mathematical physics Vol. 197; no. 2; pp. 1572 - 1591
• Main Author: Shapovalov, V. N.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-11-2018; Springer Nature B.V
• Subjects: Applications of Mathematics; Classification; Differential equations; Dirac equation; Electromagnetic fields; Electromagnetism; Mathematical and Computational Physics; Operators; Physics; Physics and Astronomy; Relativistic particles; Symmetry; Tensors; Theoretical; Riemannian space; symmetry operator; Dirac–Fock equation; Dirac equation
• ISSN: 0040-5779; 1573-9333
• DOI: 10.1134/S0040577918110028

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
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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.