Tetrahedron equation and the algebraic geometry
High Energy Physics - Theory
2008-02-03 v1 General Relativity and Quantum Cosmology
Algebraic Geometry
Abstract
The tetrahedron equation arises as a generalization of the famous Yang--Baxter equation to the 2+1-dimensional quantum field theory and the 3-dimensional statistical mechanics. Very little is still known about its solutions. Here a systematic method is described that does produce non-trivial solutions to the tetrahedron equation with spin-like variables on the links. The essence of the method is the use of the so-called tetrahedral Zamolodchikov algebras.
Keywords
Cite
@article{arxiv.hep-th/9401076,
title = {Tetrahedron equation and the algebraic geometry},
author = {I. G. Korepanov},
journal= {arXiv preprint arXiv:hep-th/9401076},
year = {2008}
}
Comments
12 pages, to appear in ``Zapiski Nauchnyh Seminarov POMI'', S-Petersburg (English translation of a part of the author's Ph.D. Thesis, S-Petersburg, 1990)