The Yang-Baxter relation and gauge invariance

TL;DR

This paper constructs a new operator solution to the Yang-Baxter equation using quantum dilogarithms over self-dual LCA groups, and introduces a gauge-invariant lattice QFT model of IRF-type based on this framework.

Contribution

It presents a novel operator solution to the Yang-Baxter equation and a new non-operator interpretation, leading to a gauge-invariant lattice QFT model.

Findings

Operator solution generalizes Faddeev-Volkov model

Provides a non-operator interpretation via Weil transformation

Constructs a gauge-invariant IRF-type lattice QFT model

Abstract

Starting from a quantum dilogarithm over a Pontryagin self-dual LCA group $A$, we construct an operator solution of the Yang-Baxter equation generalizing the solution of the Faddeev-Volkov model. Based on a specific choice of a subgroup $B\subset A$ and by using the Weil transformation, we also give a new non-operator interpretation of the Yang-Baxter relation. That allows us to construct a lattice QFT-model of IRF-type with gauge invariance under independent $B$-translations of local `spin' variables.