Pure SU(3) lattice gauge theory using operators and states

TL;DR

This paper presents a nonperturbative approach to pure SU(3) gauge theory on a large lattice using Schrödinger's equation, identifying gauge-invariant excitations and comparing excitation energies to known results.

Contribution

It introduces a basis of approximately 1000 states and a method to recover gauge invariance through extrapolation, providing new insights into the spectrum of SU(3) gauge theory.

Findings

Successful identification of gauge-invariant excitations

Approximate excitation energies match known results in weak coupling

Method applicable to glueball regime

Abstract

We study pure SU(3) gauge theory on a large lattice, using Schrodinger's equation. Our approximate solution uses a basis of roughly 1000 states. Gauge invariance is recovered when the color content of the ground state is extrapolated to zero. We are able to identify the gauge invariant excitations that remain when the extrapolation is performed. In the weak coupling limit, we obtain promising results when we compare the excitation energies (masses) to known results, which we derive. We discuss the application of our nonperturbative method to the regime where glueballs are present.