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

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

1997-11-26

arxiv.org/abs/hep-th/9711189v1

Int.J.Mod.Phys. A13 (1998) 5219-5244

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, 11 figures, LaTeX

Scientific paper

10.1142/S0217751X98002390

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.

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