Gauge field copies

TL;DR

This paper explores Wu-Yang ambiguities in 3D gauge fields, linking them to torsion-free dreibeins, and shows that any smooth Yang-Mills tensor can be uniquely expressed as a non-Abelian magnetic field.

Contribution

It establishes a connection between Wu-Yang ambiguities and torsion-free dreibeins, and demonstrates the unique representation of Yang-Mills tensors as magnetic fields in three dimensions.

Findings

Wu-Yang ambiguities are boundary condition issues in 3D.

Any smooth Yang-Mills tensor in 3D can be uniquely expressed as a non-Abelian magnetic field.

Abstract

The problem of Wu-Yang ambiguities in 3 dimensions is related to the problem of existence of torsion free driebeins for an arbitrary potential. The ambiguity is only at the level of boundary conditions. We also find that in 3 dimensions any smooth Yang-Mills field tensor can be uniquely written as the non-Abelian magnetic field of a smooth Yang-Mills potential.