Tetrahedron equation and the 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.

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)

Cited by in corpus (6)

• Let's Baxterise
• Super-Hubbard models and applications
• Classical integrable field theories in discrete 2+1 dimensional space-time
• Particles and strings in a (2+1)-D integrable quantum model
• On integrability of the one-dimensional Hubbard model
• Some eigenstates for a model associated with solutions of tetrahedron equation. III. Tetrahedral Zamolodchikov algebras and perturbed strings