Equivalence of the Beta-function of the Variational Approach to that of QCD

TL;DR

This paper demonstrates that a variational approach to QCD captures the dominant anti-screening behavior responsible for asymptotic freedom, linking it to Coulomb interaction renormalization by gluons.

Contribution

It shows how the variational ansatz reproduces the key anti-screening contribution to the QCD beta-function and clarifies the physical origins of screening effects.

Findings

Anti-screening contribution of -4 originates from Coulomb interaction renormalization.

Lesser screening of 1/3 arises from transverse gluon interactions.

Variational ansatz must include full gluon dynamics to accurately capture QCD running coupling.

Abstract

The variational ansatz for the ground state wavefunctional of QCD is found to capture the anti-screening behaviour that contributes the dominant `-4' to the beta-function and leads to asymptotic freedom. By considering an SU(N) purely gauge theory in the Hamiltonian formalism and choosing the Coulomb gauge, the origins of all screening and anti-screening contributions in gluon processes are found in terms of the physical degrees of freedom. The overwhelming anti- screening contribution of `-4' is seen to originate in the renormalisation of a Coulomb interaction by a transverse gluon. The lesser screening contribution of `1/3' is seen to originate in processes involving transverse gluon interactions. It is thus apparent how the variational ansatz must be developed to capture the full running of the QCD coupling constant.