Exploring gauge-invariant vacuum wave functionals for Yang-Mills theory

TL;DR

This paper develops gauge-invariant approximations to the Yang-Mills vacuum wave functional, revealing phenomena like dimensional transmutation, gluon condensation, and a dynamical mass gap, while introducing novel infrared degrees of freedom and insights into gauge-invariant excitations.

Contribution

It introduces a new gauge-invariant variational approach to Yang-Mills theory that captures infrared dynamics and identifies universal gauge-invariant degrees of freedom.

Findings

Emergence of dimensional transmutation and gluon condensation.

Identification of gauge-invariant saddle-point fields.

Insights into instanton stabilization and Faddeev-Niemi knots.

Abstract

We study gauge-invariant approximations to the Yang-Mills vacuum wave functional in which asymptotic freedom and a detailed description of the infrared dynamics are encoded through squeezed core states. After variationally optimizing these trial functionals, dimensional transmutation, gluon condensation and a dynamical mass gap of the expected magnitude emerge transparently. The dispersion properties of the soft gauge modes are modified by higher-gradient interactions and suggest a negative differential color resistance of the Yang-Mills vacuum. Casting the soft-mode dynamics into the form of an effective action for gauge-invariant collective fields, furthermore, allows to identify novel infrared degrees of freedom. The latter are gauge-invariant saddle-point fields which summarize dominant and universal contributions from various gauge-field orbits to all amplitudes. Their analysis provides new insights into how the vacuum gluon fields generate gauge-invariant excitations. Examples include a dynamical size stabilization mechanism for instantons and merons, a gauge-invariant representation of their effects as well as a new physical interpretation for Faddeev-Niemi knots.