Gauge theories from scattering amplitudes with minimal assumptions

TL;DR

This paper demonstrates that gauge symmetries in theories with massless particles naturally emerge from the fundamental properties of scattering amplitudes, without relying on prior assumptions about coupling constants.

Contribution

It shows that symmetry and reality properties of couplings are derived from consistent four-particle amplitude factorization, not assumed, extending to gravity interactions.

Findings

Coupling properties arise from amplitude factorization

CP invariance is a derived property

Method applies to gauge and gravity theories

Abstract

We revisit the emergence of a Yang-Mills symmetry in theories with massless spin 1 particles from fundamental physical properties of scattering amplitudes. In the standard proofs, some symmetry and reality properties of the coupling constants in three-point amplitudes are assumed. These properties cannot be justified using only three-point amplitudes but we show that they arise as consequences of the consistent factorization of four-particle amplitudes, for particular choices of the particle basis. This applies to self-interactions of massless spin 1 particles and also to their interactions with spin 0 and 1/2 particles. CP invariance is a derived property, not an additional assumption. The situation for gravity interactions is analogous and it is dealt with in the same fashion.