A variational approach to the QCD wavefunctional: Calculation of the QCD beta-function

TL;DR

This paper presents a variational method to calculate the QCD beta-function from a vacuum wavefunctional ansatz, revealing asymptotic freedom and differences in the beta-function coefficient due to gluon contributions.

Contribution

It introduces a variational approach to compute the QCD beta-function directly from the vacuum wavefunctional, highlighting the impact of gluon contributions and the Gauss law constraint.

Findings

The beta-function is asymptotically free in both the ansatz and QCD.

The coefficient differs by 1/3 due to omitted transverse gluons.

Renormalization is interpreted through non-local Feynman diagrams.

Abstract

The beta-function is calculated for an SU(N) Yang-Mills theory from an ansatz for the vacuum wavefunctional. Direct comparison is made with the results of calculations of the beta-function of QCD. In both cases the theories are asymptotically free. The only difference being in the numerical coefficient of the beta-function, which is found to be -4 from the ansatz and -4+1/3 from other QCD calculations. This is because, due to the constraint of Gauss' law applied to the wavefunctional, transverse gluons (which contribute the 1/3) are omitted. The renormalisation procedure is understood in terms of `tadpole' and `horse-shoe' Feynman diagrams which must be interpreted with a non-local propagator.