2002/08/31 by G. von Gehlen, G von Gehlen, S. Pakuliak +2 · 2 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #hep-th #nlin.SI
paper · pdf · doi:10.1088/0305-4470/36/4/309
published as J.Phys.A36:975-998,2003 · 28 pages, 3 figures
arxiv created 2002/10/31 · openalex publication_date 2003/01/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at N-th root of unity is solved by a rational mapping operator which is obtained from the solution of a linear problem. We show that the solutions can be parameterized in terms of eight free parameters and sixteen discrete phase choices, thus providing a broad starting point for the construction of 3-dimensional integrable lattice models. The Fermat curve points parameterizing the representation of the mapping operator in terms of cyclic functions are expressed in terms of the independent parameters. An explicit formula for the density factor of the MTE is derived. For the example N=2 we write the MTE in full detail. We also discuss a solution of the MTE in terms of bosonic continuum functions.