Equal-time two-point correlation functions in Coulomb gauge Yang–Mills theory

Abstract

We apply a functional perturbative approach to the calculation of the equal-time two-point correlation functions and the potential between static color charges to one-loop order in Coulomb gauge Yang–Mills theory. The functional approach proceeds through a solution of the Schrödinger equation for the vacuum wave functional to order g 2 and derives the equal-time correlation functions from a functional integral representation via new diagrammatic rules. We show that the results coincide with those obtained from the usual Lagrangian functional integral approach, extract the beta function, and determine the anomalous dimensions of the equal-time gluon and ghost two-point functions and the static potential under the assumption of multiplicative renormalizability to all orders.