Abstract
In this paper new exact solutions for the Dirac equation are presented for the case of a particle in tensor wave field on the background of gravitation. Consideration is given to different configurations introducing the tensor interaction, which result in the required separation of variables by the algebraic method and lead to the derivation of exact solutions for the Dirac equation in the corresponding field situation. At the same time, most general metrics allowing for the exact solutions are given. The cases of zero and nonzero rest mass of a particle are with treated here.
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