Quantum Holonomy in Three-dimensional General Covariant Field Theory and Link Invariant

TL;DR

This paper demonstrates that quantum holonomy in a three-dimensional covariant non-Abelian field theory acts as a topological link invariant, maintaining metric independence after gauge fixing, and explores its relation to link polynomials.

Contribution

It confirms that quantum holonomy retains topological properties in a covariant gauge-fixed setting and relates it to link invariants and polynomials, extending previous results.

Findings

Quantum holonomy is metric independent after gauge fixing.

Quantum holonomy acts as a link invariant.

Relation established between quantum holonomy and link polynomials.

Abstract

We consider quantum holonomy of some three-dimensional general covariant non-Abelian field theory in Landau gauge and confirm a previous result partially proven. We show that quantum holonomy retains metric independence after explicit gauge fixing and hence possesses the topological property of a link invariant. We examine the generalized quantum holonomy defined on a multi-component link and discuss its relation to a polynomial for the link.