Symmetry operators and separation of variables in the $(2+1)$-dimensional Dirac equation with external electromagnetic field

Abstract

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a $(2+1)$-dimensional Minkowski (flat) space. For each of the sets we carry out a complete separation of variables in the Dirac equation and find a corresponding electromagnetic potential permitting separation of variables.

arXiv comment24 pages, version accepted for publication in Int. J. Geom. Methods Mod. Phys

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Cited by in corpus (2)

• Algebras of integrals of motion for the Hamilton-Jacobi and Klein-Gordon-Fock equations in spacetime with a four-parameter groups of motions in the presence of an external electromagnetic field
• Maxwell equations in homogeneous spaces with solvable groups of motions