Poincaré 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'' \(q\) characterising the fields approximating the gluon c...

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Bibliographic Details
Published in:arXiv.org 2006-01
Main Authors: Kalloniatis, A C, Nedelko, S N
Format: Article
Language:English
Subjects:
Existence theorems
Irrationality
Partitions (mathematics)
Quantum chromodynamics
Online Access:Get full text
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Summary: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'' \(q\) 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 \(U_{\rm A}(1)\) 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.
ISSN:2331-8422
DOI:10.48550/arxiv.0503168