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 representations for the Dirac propagator we get representations with a spin factor in an arbitrary external field. Thus, the propagator appears to be presented by means of a bosonic path integral only. Then we use the representations 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.

• Received 27 August 1996

DOI:https://doi.org/10.1103/PhysRevD.55.7701