SPIN FACTOR IN THE PATH-INTEGRAL REPRESENTATION FOR THE DIRAC PROPAGATOR IN EXTERNAL FIELDS

We study the problem of the spin factor both in 3+1 and 2+1 dimensions , two cases which are essentially different in this respect. Doing all Grassmann integrations in the corresponding path integral representat ions for the Dirac propagator we get representations with a spin facto r in an arbitrary external field. Thus, the propagator appears to be p resented by means of a bosonic path integral only. Then we use the rep resentations with a spin factor for calculations of the propagator in some configurations of external fields: namely, in a constant uniform electromagnetic field and in its combination with a plane wave field.