Beyond Complex Langevin Equations: positive representation of a class of complex measures

TL;DR

This paper develops a positive representation method for certain complex measures, especially on U(1) groups, with applications demonstrated in abelian lattice gauge theories.

Contribution

It introduces new explicit realizations of positive representations for complex measures on U(1) groups, expanding the tools for handling complex densities.

Findings

Constructed positive representations for complex measures on U(1) groups.

Identified general conditions for such representations.

Demonstrated applications in abelian lattice gauge theories.

Abstract

A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of U(1) groups are studied. After identifying general conditions which such representations should satisfy, several explicit realizations are proposed. Their utility is illustrated in few concrete examples representing problems in abelian lattice gauge theories.