On the invariant measure for the Yang-Mills configuration space in (3+1) dimensions

TL;DR

This paper investigates the gauge-invariant configuration space of 3+1 dimensional Yang-Mills theories, developing an approximate volume element calculation and estimating glueball mass ratios through comparisons with lower-dimensional models.

Contribution

It introduces a matrix parametrization for gauge potentials in 3+1 dimensions and provides an approximate method to compute the volume element on the gauge-invariant space.

Findings

Developed an approximate calculation of the volume element.

Estimated the ratio of $0^{++}$ glueball mass to string tension.

Compared results with (2+1)-dimensional Yang-Mills theory.

Abstract

We consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parametrized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom. We develop an approximate calculation of the volume element on the gauge-invariant configuration space. We also make a rough estimate of the ratio of $0^{++}$ glueball mass and the square root of string tension by comparison with $(2+1)$-dimensional Yang-Mills theory.