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Symmetry operators and separation of variables in the (2+1)(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)(2+1)-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a (2+1)(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.Comment: 24 pages, version accepted for publication in Int. J. Geom. Methods Mod. Phy

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