Evolution equations for the quark-meson transition

Evolution equations describe the effect of consecutively integrating out all quantum fluctuations with momenta larger than some infrared cutoff scale k. We develop a formalism for the introduction of collective degrees of freedom at some intermediate scale and derive the corresponding evolution equations. This allows us to account for the appearance of bound states at some characteristic length scale as, for example, the mesons in QCD. The vacuum properties, including condensates of composite operators, can be directly inferred from the effective action for k → 0. We compute in a simple QCD-motivated model with four-quark interactions the chiral condensate overlineψψ and the effective action for pions including ƒ _π. A full treatment of QCD along these lines seems feasible but still requires substantial work.