Variational solution of the Yang-Mills Schr\"odinger equation in Coulomb gauge

TL;DR

This paper presents a variational approach to solving the Yang-Mills Schrödinger equation in Coulomb gauge, deriving coupled equations for propagators and revealing confinement-related infrared behavior.

Contribution

It introduces a variational ansatz peaked at the Gribov horizon and derives coupled Schwinger-Dyson equations for the Yang-Mills vacuum in Coulomb gauge.

Findings

Infrared suppressed gluon propagator

Infrared singular ghost propagator

Almost linearly rising confinement potential

Abstract

The Yang-Mills Schr\"odinger equation is solved in Coulomb gauge for the vacuum by the variational principle using an ansatz for the wave functional, which is strongly peaked at the Gribov horizon. A coupled set of Schwinger-Dyson equations for the gluon and ghost propagators in the Yang-Mills vacuum as well as for the curvature of gauge orbit space is derived and solved in one-loop approximation. We find an infrared suppressed gluon propagator, an infrared singular ghost propagator and a almost linearly rising confinement potential.