Unitary Background Gauges and Hamiltonian approach to Yang--Mills Theories

TL;DR

This paper explores specific unitary gauges in background field perturbation theory to facilitate a Hamiltonian approach to Yang--Mills theories, deriving propagators and discussing applications to QCD confinement phenomena.

Contribution

It introduces two suitable gauges for Hamiltonian treatment in Yang--Mills theories and derives their propagators, enabling better analysis of QCD at the confinement scale.

Findings

Derived propagators for gluonic fluctuations in selected gauges.

Identified gauges that simplify Hamiltonian analysis of Yang--Mills theories.

Discussed potential applications to QCD spectrum and hybrid states.

Abstract

A variety of unitary gauges for perturbation theory in a background field is considered in order to find those most suitable for a Hamiltonian treatment of the system. We select two convenient gauges and derive the propagators $D_{\mu\nu}$ for gluonic quantum fluctuations immersed in background configurations. The first one is a unitary generalization of the usual Coulomb gauge in QED which preserves the decoupling of two propagating polarizations from the instantaneous one. The second possibility is the axial light cone gauge which remains ghost free also in the presence of a background. Applications of the formalism to the spectrum and dynamics of QCD at the confinement scale, such as hybrid states, are briefly discussed.