Quantum geometry of three-dimensional lattices
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Bazhanov, Vladimir; Mangazeev, Vladimir; Sergeev, Sergey
Description
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]
Collections | ANU Research Publications |
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Date published: | 2008 |
Type: | Journal article |
URI: | http://hdl.handle.net/1885/24035 |
Source: | Journal of Statistical Mechanics: Theory and Experiment |
DOI: | 10.1088/1742-5468/2008/07/P07004 |
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01_Bazhanov_Quantum_geometry_of_2008.pdf | 1.4 MB | Adobe PDF | Request a copy |
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