General Spin Sums in Quantum Field Theory

TL;DR

This paper investigates the possibility of generalizing spin and polarization sums in quantum field theory, aiming to extend the standard methods used for fermionic fields to a broader, more general framework.

Contribution

It derives the most general form of spin sums for fermionic fields within quantum field theory, expanding beyond traditional plane-wave solutions.

Findings

Derived the most general fermionic spin sums

Extended the Michel-Wightman identities

Provided a framework for generalized propagator calculations

Abstract

In Quantum Field Theory, scattering amplitudes are computed from propagators which, for internal lines, are built upon spin/polarization-sum relationships. In turn, these are normally constructed upon plane-wave solutions of the free field equations. A question that may now arise is whether such spin/polarization-sums can be generalized. In the past, there has been a first attempt at generalizing spin sums for fermionic fields in terms of the Michel-Wightman identities. In this paper, we aim to find the most general spin sums for fermionic fields within the range of QFT.