Gauge-invariant soft modes in Yang-Mills theory

TL;DR

This paper introduces a gauge-invariant approach to analyze soft modes in Yang-Mills theory, revealing how vacuum fields form collective excitations and providing a new perspective on instantons, merons, and Faddeev-Niemi knots.

Contribution

It develops a gauge-invariant saddle point expansion for the Yang-Mills vacuum, identifying dominant infrared degrees of freedom for analytical soft amplitude analysis.

Findings

Identification of gauge-invariant infrared degrees of freedom.

Representation of instanton and meron effects in a gauge-invariant manner.

New physical interpretation for Faddeev-Niemi knots.

Abstract

A gauge-invariant saddle point expansion for the Yang-Mills vacuum transition amplitude on the basis of the squeezed approximation to the vacuum wave functional is outlined. This framework allows the identification of gauge-invariant infrared degrees of freedom which arise as dominant sets of gauge field orbits and provide the principal input for an essentially analytical treatment of soft amplitudes. The analysis of the soft modes sheds new light on how vacuum fields organize themselves into collective excitations and yields a gauge-invariant representation of instanton and meron effects as well as a new physical interpretation for Faddeev-Niemi knots.