The Yang-Baxter relation and gauge invariance

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.

16 pages

References in corpus (4)

• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• Operators from mirror curves and the quantum dilogarithm
• Exact solution of the Faddeev-Volkov model
• Q-operators in the six-vertex model

Cited by in corpus (6)

• Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
• Lens partition function, pentagon identity and star-triangle relation
• General modular quantum dilogarithm and beta integrals
• On the separation of variables for the modular XXZ magnet and the lattice Sinh-Gordon models
• Quasi-classical expansion of a hyperbolic solution to the star-star relation and multicomponent 5-point difference equations
• Exactly Solved Models and Beyond: a special issue in honour of R J Baxter's 75th birthday