The Physical Hilbert Space of SU(2) Lattice Gauge Theory

TL;DR

This paper introduces a new method to explicitly construct the physical Hilbert space of SU(2) lattice gauge theory using harmonic oscillator prepotentials, providing a gauge-invariant basis in closed form.

Contribution

It develops a harmonic oscillator prepotential approach to solve the Gauss law and constructs a gauge-invariant orthonormal basis for SU(2) lattice gauge theory.

Findings

Explicit gauge-invariant basis constructed in closed form

Method generalizes to SU(N) gauge groups

Provides a new framework for analyzing lattice gauge theories

Abstract

We solve the Gauss law of SU(2) lattice gauge theory using the harmonic oscillator prepotential formulation. We construct a generating function of a manifestly gauge invariant and orthonormal basis in the physical Hilbert space of (d+1) dimensional SU(2) lattice gauge theory. The resulting orthonormal physical states are given in closed form. The generalization to SU(N) gauge group is discussed.