Poincaré recurrence theorem and the strong CP-problem

Abstract

The existence in the physical QCD vacuum of nonzero gluon condensates, such as $<g^2{F}^2>$, requires dominance of gluon fields with finite mean action density. This naturally allows any real number value for the unit ``topological charge'' $q$ characterising 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 $\theta$ parameter for which CP is spontaneously broken are dense in $\mathbb{R}$, which provides for a mechanism of resolving the strong CP problem simultaneously with a correct implementation of $U_{\mathrm{A}}(1)$ symmetry. We present an explicit realisation 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.

arXiv comment8 pages, RevTeX, 3 figures. Revised after referee suggestions. Now includes model independent arguments

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