Variational calculations with improved energy functionals in gauge theories

TL;DR

This paper introduces an improved variational method for SU(N) Yang-Mills theories using gauge-invariant Gaussian wave functionals, accurately capturing the interaction energy and reproducing the one-loop beta function.

Contribution

It develops a variational approach with gauge-invariant projections that accurately computes energies and reproduces known perturbative results in gauge theories.

Findings

Consistent ultraviolet behavior with perturbation theory

Reproduction of the one-loop beta function

Effective calculation of interaction energies in external fields

Abstract

For a SU(N) Yang-Mills theory, we present variational calculations using gaussian wave functionals combined with an approximate projection on gauge invariant states. The projection amounts to correcting the energy of the gaussian states by substracting the spurious energy associated with gauge rotations. Based on this improved energy functional, we perform variational calculations of the interaction energy in the presence of external electric and magnetic fields. We verify that the ultraviolet behaviour of our approximation scheme is consistent, as it should, with that expected from perturbation theory. In particular, we recover in this variational framework the standard one-loop beta function, with a transparent interpretation of the screening and anti-screening contributions.