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.
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