Covariant path integral for the Dirac equation with pseudoscalar potentials

The problem of a relativistic spinning particle interacting with pseudoscalar potentials in (3 + 1) dimensions is formulated in the framework of covariant supersymmetric path integrals. The relative Green's function is expressed through a functional integral over bosonic trajectories that describe the external motion and fermionic variables that describe the spin degrees of freedom. As an application, we have considered the case of the plane wave, where the pseudoscalar potential is an arbitrary function of the variable (kμxμ). The (3 + 1)-dimensional problem is reduced to a (1 + 1)-dimensional one by using an identity. For the case of k2 = 0, the relative propagator is exactly calculated and the wavefunctions are extracted