The modified tetrahedron equation and its solutions

Gunter Von Gehlen, Stanislav Pakuliak, S. Sergeev

Research output: Contribution to journalArticle

3 Citations (Scopus)

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
Volume19
Issue numberSUPPL. 2
Publication statusPublished - May 2004
Externally publishedYes

Fingerprint

Triangular pyramid
tetrahedrons
operators
Operator
Gauss equation
Fermat Curve
Weyl Algebra
Spin Models
Roots of Unity
Conjugation
Lattice Model
conjugation
Invertible
Gauss
Branching
unity
invariance
Invariance
algebra
Decompose

Cite this

Von Gehlen, G., Pakuliak, S., & Sergeev, S. (2004). The modified tetrahedron equation and its solutions. International Journal of Modern Physics A, 19(SUPPL. 2), 179-204.
Von Gehlen, Gunter ; Pakuliak, Stanislav ; Sergeev, S. / The modified tetrahedron equation and its solutions. In: International Journal of Modern Physics A. 2004 ; Vol. 19, No. SUPPL. 2. pp. 179-204.
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Von Gehlen, G, Pakuliak, S & Sergeev, S 2004, 'The modified tetrahedron equation and its solutions', International Journal of Modern Physics A, vol. 19, no. SUPPL. 2, pp. 179-204.

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

In: International Journal of Modern Physics A, Vol. 19, No. SUPPL. 2, 05.2004, p. 179-204.

Research output: Contribution to journalArticle

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Von Gehlen G, Pakuliak S, Sergeev S. The modified tetrahedron equation and its solutions. International Journal of Modern Physics A. 2004 May;19(SUPPL. 2):179-204.