Integration of the Dirac Equation on Lie Groups in an External Electromagnetic Field Admitting a Noncommutative Symmetry Algebra

Abstract

Noncommutative integration of the Dirac equation on Lie groups with a right-invariant metric and an invariant electromagnetic field tensor is considered. An electromagnetic field, admitting a noncommutative reduction of the Dirac equation, but not admitting either diagonalization of the squared Dirac equation or separation of variables, is found.