Positive Representations of a Class of Complex Measures

Abstract

We study the problem of constructing positive representations of complex measures. In this paper we consider complex densities on a direct product of $U(1)$ groups and look for representations by probability distributions on the complexification of those groups. After identifying general necessary and sufficient conditions we propose several concrete realizations. Finally we study some of those realizations in examples representing problems in abelian lattice gauge theories.

Comments: 19 pages, 3 figures, minor changes to bring it into agreement with published version