Geodesic
Symmetry and classification of the~Dirac--Fock equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 2, pp. 208-229

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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–Fock equation.
Mots-clés : Dirac equation 
@article{TMF_2018_197_2_a1,
     author = {V. N. Shapovalov},
     title = {Symmetry and classification of {the~Dirac--Fock} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {208--229},
     publisher = {mathdoc},
     volume = {197},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_197_2_a1/}
}
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V. N. Shapovalov. Symmetry and classification of the~Dirac--Fock equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 2, pp. 208-229. http://geodesic.mathdoc.fr/item/TMF_2018_197_2_a1/