The (1+1) Dimensional Dirac Equation With Pseudoscalar Potentials: Path Integral Treatment

The supersymetric path integrals in solving the problem of relativistic spinning particle interacting with pseudoscalar potentials is examined. The relative propagator is presented by means of path integral, where the spin degrees of freedom are described by odd Grassmannian variables and the gauge invariant part of the effective action has a form similar to the standard pseudoclassical action given by Berezin and Marinov. After integrating over fermionic variables (Grassmannian variables), the problem is reduced to a nonrelativistic one with an effective supersymetric potential. Some explicit examples are considered, where we have extracted the energy spectrum of the electron and the wave functions. PACS numbers: 03.65. Ca-Formalism, 03.65. Db-Functional analytical methods, 03.65. Pm-Relativistic wave equations.