EVOLUTION-EQUATIONS FOR THE QUARK MESON TRANSITION

Evolution equations describe the effect of consecutively integrating o ut all quantum fluctuations with momenta larger than some infrared cut off scale k. We develop a formalism for the introduction of collective degrees of freedom at some intermediate scale and derive the correspo nding evolution equations. This allows us to account for the appearanc e of bound states at some characteristic length scale as, for example, the mesons in QCD. The vacuum properties, including condensates of co mposite operators, can be directly inferred from the effective action for k --> 0. We compute in a simple QCD-motivated model with four-quar k interactions the chiral condensate psipsiBAR and the effective actio n for pions including f(pi). A full treatment of QCD along these lines seems feasible but still requires substantial work.