  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.
