The modified tetrahedron equation amd its solutions

Gunter Von Gehlen, Stanislav Pakuliak, Sergey Sergeev

Research output: Contribution to journalArticle

Abstract

A large class of 3-dimensional integrable lattice spin models is constructed. The starting point is an invertible canonical mapping operator R1,2,3 in the space of a triple Weyl algebra. R1,2,3 is derived postulating a current branching principle together with a Baxter Z-invariance. The tetrahedron equation for R1,2,3 follows without further calculation. If the Weyl parameter is taken to be a root of unity, R1,2,3 decomposes into a matrix conjugation operator R 1,2,3 and a c-number functional mapping R1,2,3(f). The operator R1,2,3 satisfies a modified tetrahedron equation (MTE) in which the "rapidities" are solutions of a classical integrable Hirota-type equations. R1,2,3 can be represented in terms of the Bazhanov-Baxter Fermat curve cyclic functions, or alternatively in terms of Gauss functions. The paper summarizes several recent publications on the subject
Original languageEnglish
Pages (from-to)179-204
Number of pages26
JournalInternational Journal of Modern Physics A
VolumeA19S2
Publication statusPublished - 2004
Externally publishedYes

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tetrahedrons
operators
Gauss equation
conjugation
unity
invariance
algebra
curves
matrices

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Von Gehlen, G., Pakuliak, S., & Sergeev, S. (2004). The modified tetrahedron equation amd its solutions. International Journal of Modern Physics A, A19S2, 179-204.
Von Gehlen, Gunter ; Pakuliak, Stanislav ; Sergeev, Sergey. / The modified tetrahedron equation amd its solutions. In: International Journal of Modern Physics A. 2004 ; Vol. A19S2. pp. 179-204.
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Von Gehlen, G, Pakuliak, S & Sergeev, S 2004, 'The modified tetrahedron equation amd its solutions', International Journal of Modern Physics A, vol. A19S2, pp. 179-204.

The modified tetrahedron equation amd its solutions. / Von Gehlen, Gunter; Pakuliak, Stanislav; Sergeev, Sergey.

In: International Journal of Modern Physics A, Vol. A19S2, 2004, p. 179-204.

Research output: Contribution to journalArticle

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AU - Pakuliak, Stanislav

AU - Sergeev, Sergey

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