Field Configurations and the SU(2) Haar Measure in QCD

TL;DR

This paper investigates specific SU(2) gluonic field configurations in a modified axial gauge, revealing implications for gluonic wavefunctionals and the presence of $ heta$ dependence in QCD.

Contribution

It characterizes a class of SU(2) field configurations where the Haar measure remains non-zero despite zero mode components, impacting boundary conditions and $ heta$ dependence in QCD.

Findings

Gluonic wavefunctionals need not vanish at the boundary of the fundamental domain.

Zero mode components can vanish at some space point without nullifying the Haar measure.

The results imply potential $ heta$ dependence in QCD(3+1).

Abstract

We characterise a class of SU(2) gluonic field configurations in the modified axial gauge where a zero mode component vanishes at some space point but the global Haar measure remains non-zero. The consequence of this is that gluonic wavefunctionals need not vanish at the boundary of the fundamental modular domain, which itself permits $\theta$ dependence in QCD(3+1).