Symmetry and Classification of the Dirac–Fock Equation
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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 V4 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.
Keywordssymmetry operator Riemannian space Dirac equation Dirac–Fock equation
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