The Infrared Behaviour of alpha_S from Mandelstam's Approximation to the Gluon Dyson-Schwinger Equation

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  • 29 April 1996
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, i.e., alpha_S increases without bound in the infrared. The non-perturbative result for an infrared singular quark interaction can be used to relate the string tension sigma to the QCD scale Lambda.

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