The Most General Propagator in Quantum Field Theory

TL;DR

This paper derives the most general form of the field propagator in quantum field theory for spinors and vectors using polar form, expanding the mathematical tools available for QFT calculations.

Contribution

It introduces the most general propagator expressions for spinors and vectors, generalizing previous specific forms in quantum field theory.

Findings

Derived the general propagator for spinors using polar form

Provided a comprehensive discussion for vector propagators

Expanded the mathematical framework for QFT calculations

Abstract

One of the most important mathematical tools necessary for Quantum Field Theory calculations is the field propagator. Applications are always done in terms of plane waves and although this has furnished many magnificent results, one may still be allowed to wonder what is the form of the most general propagator that can be written. In the present paper, by exploiting what is called polar form, we find the most general propagator in the case of spinors, whether regular or singular, and we give a general discussion in the case of vectors.