Tetrahedron equation and the algebraic geometry

Details Tetrahedron equation and the algebraic geometry Tetrahedron equation and the algebraic geometry

1994-01-17

arxiv.org/abs/hep-th/9401076v1

Zapiski Nauchn. Semin. POMI (S-Petersburg) 209 (1994) 137-149

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, to appear in ``Zapiski Nauchnyh Seminarov POMI'', S-Petersburg (English translation of a part of the author's Ph.D.

Scientific paper

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.

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