Implementing Gauss's law in Yang-Mills theory and QCD

TL;DR

This paper develops a transformation to enforce Gauss's law in Yang-Mills theory and QCD, highlighting its non-unitary nature and implications for the S-matrix and Feynman rules.

Contribution

It introduces a non-unitary transformation that converts perturbative states into physical states satisfying Gauss's law in Yang-Mills and QCD.

Findings

The transformation is inherently non-unitary.

Unitarily equivalent states reproduce standard S-matrix elements.

Non-unitary states have distinct physical implications.

Abstract

We construct a transformation that transforms perturbative states into states that implement Gauss's law for `pure gluonic' Yang-Mills theory and QCD. The fact that this transformation is not and cannot be unitary has special significance. Previous work has shown that only states that are unitarily equivalent to perturbative states necessarily give the same S-matrix elements as are obtained with Feynman rules.