General spin sums in Quantum Field Theory

Abstract

In Quantum Field Theory (QFT), 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.