A class of toy (functional) universal models with confining « monopole » configurations

Summary

Inspired by the path integral formulation of field theory, a generating functional is defined which gives rise to an algebraic representation of the correlation of field operators. A class of toy models is constructed which share a universality property in the sense that they all lead to the same expression for the correlation function 〈μ(x₁) ...μ(x_n)〉 of a certain operator self-consistently defined, and the latter correlation function is zero if there is any odd number of coincident (that is equal) x-points in [x₁, ..., x_n]. This gives rise to a clustering property, with the clusters localized at different x-points, and the number of fields in each cluster being necessarily even. The connection of this work with local field theory is discussed.