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

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.