Dirac particle in the presence of a plane waveand constant magnetic fields: path integral approach

The Green function (GF) related to the problem of a Dirac particle interacting with a plane wave and constant magnetic fields is calculated in the framework of a path integral via the Alexandrou et al. formalism according to the so-called global projection. As a calculation tool, we introduce two identities (constraints) into this formalism; their main role is the reduction of the dimension of the integral and the emergence in a natural way of some classical paths and, due to the existence of a constant electromagnetic field, we have used the technique of fluctuations. Hence the calculation of the GF is reduced to a known Gaussian integral plus a contribution from the effective classical action.