The infrared behaviour of αs from Mandelstam's approximation to the 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 β 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., αs increases without bound in the infrared. The non-perturbative result for an infrared singular quark interaction can be used to relate the string tension σ to the QCD scale Λ. 3 refs., 1 fig