Exactsolution of Dirac and Klein-Gordon-Fock equations in a curved spaceadmitting a second Dirac operator

Abstract

We give a brief review of integrationmethods of relativistic wave equations incurved spaces. On the basis of anon-commutative integration method we givean exact solution of Dirac andKlein-Gordon-Fock equations in afour-dimensional Ricci flat manifoldadmitting a second Dirac operator. Someanalytical properties of the solutions arestudied. We compare spectra of spin andscalar particles as well. A visual model ofthe supersymmetry structure which arisesis considered and the physical sense of thesecond Dirac operator is explained.