Scalar and spinning particles in a plane wave field

TL;DR

This paper investigates the quantization of relativistic scalar and spinning particles in a plane wave electromagnetic field using path integrals, providing explicit propagator calculations and a proof of amplitude determination.

Contribution

It introduces a rigorous method for quantizing spinning particles with Grassmann variables in a plane wave field and explicitly computes the propagators.

Findings

Feynman amplitudes depend solely on classical contributions

Explicit forms of propagators for scalar and spinning particles

Validation of the path integral approach in this context

Abstract

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 rigourous proof that the Feynman amplitudes are only determined by the classical contribution and we explicitly evaluate the propagators.