The strong running coupling from an approximate gluon Dyson-Schwinger equation

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 behavior 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}{sub S} increases without bound in the infrared.