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Quantum geometry of three-dimensional lattices

Bazhanov, Vladimir; Mangazeev, Vladimir; Sergeev, Sergey


We study geometric consistency relations between angles on three-dimensional (3D) circular quadrilateral lattices - lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical transformations of a remarkable 'ultra-local' Poisson bracket algebra defined on discrete 2D surfaces consisting of circular quadrilaterals. Quantization of this structure leads to new solutions of the tetrahedron equation (the 3D analog of the Yang-Baxter...[Show more]

CollectionsANU Research Publications
Date published: 2008
Type: Journal article
Source: Journal of Statistical Mechanics: Theory and Experiment
DOI: 10.1088/1742-5468/2008/07/P07004


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