Confinement and the cluster decomposition property in QCD

The behaviour of correlators at large distances plays an important role in QCD. In particular, if correlators consisting of clusters of coloured fields are non-vanishing for space-like asymptotic distances, then this implies that the strength of the correlations between the coloured degrees of freedom in these clusters increases at large distances, which is a sufficient condition for confinement. Correlators with this property are said to violate the cluster decomposition property (CDP). Here we discuss a rigorous approach to establish a general criterion for when the CDP is violated. By applying this criterion to QCD, it turns out that certain lattice results involving the quark and gluon propagators can be interpreted as evidence that quarks and gluons are confined due to a violation of the CDP.