q--exchangeable Measures and Transformations in Interacting Particle Systems

TL;DR

This paper develops a unified framework for analyzing measures and transformations in interacting particle systems, introducing conditions for reversibility and gauge transformations, and employing quantum groups to establish these conditions.

Contribution

It introduces a general method using quantum groups to verify conditions for reversibility and transformations in particle systems, specializing to q-exchangeability.

Findings

Established conditions for reversibility and gauge transformations.

Developed a method using quantum groups to verify these conditions.

Specialized conditions to q-exchangeable properties.

Abstract

This paper provides unified calculations regarding certain measures and transformations in interacting particle systems. More specifically, we provide certain general conditions under which an interacting particle system will have a reversible measure, gauge transformation, or ground state transformation. Additionally, we provide a method to prove that these conditions hold. This method uses certain quantum groups, and in that context the general conditions specialize to a \(q\)--exchangeable property.