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

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

1997-05-19

arxiv.org/abs/hep-th/9705136v2

Int.J.Mod.Phys. A14 (1999) 799

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, LaTex, 2 figs

Scientific paper

10.1142/S0217751X99000397

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.

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