Scalar and spinning particles in a plane-wave field

We study the quantization problem of relativistic scalar and spinning particles interacting with a radiation electromagnetic field by using the path integral and the external source method. The spin degrees of freedom are described in terms of Grassmann variables and the Feynman kernel is obtained through functional integration on both Bose and Fermi variables. We provide rigorous proof that the Feynman amplitudes are only determined by the classical contribution and we explicitly evaluate the propagators.