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Journal of the Physical Society of Japan

The \({\rbb Z}_{\mibs N}\) Symmetric Quantum Lattice Field Theory The Quantum Group Symmetry, the Yang–Baxter Equation, and the Integrals of Motion

Kazuhiro Hikami

Published Jan 15, 1999• 4 citations
Publisher

Abstract

We study the quantum group symmetry of the ({\bb Z}_{N}) symmetric lattice field theory, which is viewed as a discretization of the (\widehat{s\ell (N)}) affine Toda field theory. We reveal the quantum group structure, and construct explicitly the quantum local integrals of motion by use of the quantum dilogarithm function.
DOI
10.1143/jpsj.68.55

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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 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.