The Strong Running Coupling from an Approximate Gluon Dyson-Schwinger Equation

Abstract

Using Mandelstam's approximation to the gluon Dyson-Schwinger equation we calculate the gluon self-energy in a renormalisation group invariant fashion. We obtain a non-perturbative $\beta$ function. The scaling behaviour near the ultraviolet stable fixed point is in good agreement with perturbative QCD. No further fixed point for positive values of the coupling is found: ${\alpha }_S$ increases without bound in the infrared.

Comments: 4 pages, 3 figures, Contribution to the Workshop ''Quark Confinement and the Hadron Spectrum II'', Como, Italy, June 26--29, 1996, to appear in the Proceedings, ed. Nora Brambilla, World Scientific