Covariant Phase Space and Soft Factorization in Non-Abelian Gauge Theories

TL;DR

This paper investigates the infrared structure of non-abelian gauge theories using covariant phase space, revealing vacuum degeneracy, universal Hilbert space, and deriving soft gluon theorems from Ward identities.

Contribution

It introduces a covariant phase space approach to non-abelian gauge theories, uncovering vacuum degeneracy and deriving soft theorems from Ward identities.

Findings

Boundary contributions cause vacuum degeneracy.

Universal and simple vacuum Hilbert space.

Soft gluon theorems follow from Ward identities.

Abstract

We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity.