Gauge-invariant ground state for canonically quantized Yang-Mills theory

TL;DR

This paper constructs a gauge-invariant candidate ground state for quantized Yang-Mills theory using Hamilton-Jacobi methods, aiming to inform approaches in quantum gravity and avoid issues with existing states.

Contribution

It introduces a novel gauge-invariant ground state construction for Yang-Mills theory with a specific factor ordering, extending previous finite-dimensional models to field theories.

Findings

Invariance under spatial rotations and translations achieved.

Candidate ground state constructed with nonlinear normal ordering.

Boost invariance remains under investigation.

Abstract

We use Hamilton-Jacobi theory to construct a gauge-invariant zero-energy candidate ground state for canonically quantized Yang-Mills theory with a "nonlinear normal" factor ordering, generalizing an analogous ordering introduced by Moncrief and Ryan for problems with finitely many degrees of freedom. Invariance under spatial rotations and translations is immediate; boost invariance remains under investigation. The motivation is to find a model for constructing a candidate ground state in general relativity, canonically quantized a la the Ashtekar variables. We seek to avoid replicating some of the more troublesome features of the Kodama state, inherited from the Chern-Simons state.