NONPERTURBATIVE FLOW EQUATIONS IN QCD

We review the formalism of the effective average action in quantum fie ld theory which corresponds to a coarse grained free energy in statist ical mechanics. The associated exact renormalization group equation an d possible nonperturbative approximations for its solution are discuss ed. This is applied to QCD where one observes the consecutive emergenc e of mesonic bound states and spontaneous chiral symmetry breaking as the coarse graining scale is lowered. We finally present a study of th e chiral phase transition in two flavor QCD. A precision estimate of t he universal critical equation of state for the three-dimensional O(4) Heisenberg model is presented. We explicitly connect the O(4) univers al behavior near the critical temperature and zero quark mass with the physics at zero temperature and a realistic pion mass. For realistic quark masses the pion correlation length near T-c turns out to be smal ler than its zero temperature value.