A confining and asymptotically free solution for the renormalisation group invariant charge

Abstract

The central role of the invariant charge in applications of the renormalisation group to quantum chromodynamics is discussed. The general structure of the invariant charge is examined, and it is shown to be a non-singular function of q2 for all finite non-zero q2. At q2=0 and q2=+or- infinity , there is always a solution for which the invariant charge vanishes. The zero at q2=0 is interpreted as a signal of quark and gluon confinement, and the zero at q2=+or- infinity shows that QCD is asymptotically free. Some applications of these general results are discussed.