Subcritical solution of the Yang-Mills Schroedinger equation in the Coulomb gauge

TL;DR

This paper solves the Dyson-Schwinger equations in Coulomb gauge Yang-Mills theory within the subcritical regime, revealing the absence of solutions in the critical regime with infrared divergent form factors.

Contribution

It provides a variational solution to the functional Schrödinger equation in Coulomb gauge Yang-Mills theory, focusing on the subcritical regime with infrared finite form factors.

Findings

Dyson-Schwinger equations are solved self-consistently in the subcritical regime.

No solutions exist for the Dyson-Schwinger equation in the critical regime with infrared divergence.

The approach advances understanding of the infrared behavior in Coulomb gauge Yang-Mills theory.

Abstract

In the Hamiltonian approach to Coulomb gauge Yang-Mills theory, the functional Schroedinger equation is solved variationally resulting in a set of coupled Dyson-Schwinger equations. These equations are solved self-consistently in the subcritical regime defined by infrared finite form factors. It is shown that the Dyson-Schwinger equation for the Coulomb form factor fails to have a solution in the critical regime where all form factors have infrared divergent power laws.