  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 path integral via Alexandrou et al. formalism according to the
so-called global projection. As a tool of calculation, we introduce two
identities (constraints) into this formalism, their main role is the reduction
of integrals dimension and the emergence in a natural way of some classical
paths, and due to the existence of 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 of the effective classical
action.
