Poincare recurrence theorem and the strong CP problem

The existence in the physical QCD vacuum of nonzero gluon condensates, such as , requires dominance of gluon fields with finite mean action density. This naturally allows any real number value for the unit 'topological charge' q characterizing the fields approximating the gluon configurations which should dominate the QCD partition function. If q is an irrational number then the critical values of the θ parameter for which CP is spontaneously broken are dense in R, which provides for a mechanism of resolving the strong CP problem simultaneously with a correct implementation of UA(1) symmetry. We present an explicit realization of this mechanism within a QCD motivated domain model. Some model independent arguments are given that suggest the relevance of this mechanism also to genuine QCD