Explicit free parametrization of the modified tetrahedron equation

Gunter Von Gehlen, Stanislav Pakuliak, S. Sergeev

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The modified tetrahedron equation (MTE) with affine Weyl quantum variables at the Mb. root of unity is solved by a rational mapping operator which is obtained from the solution of a linear problem. We show that the solutions can be parametrized in terms of eight free parameters and 16 discrete phase choices, thus providing a broad starting point for the construction of three-dimensional integrable lattice models. The Fermat-curve points parametrizing the representation of the mapping operator in terms of cyclic functions are expressed in terms of the independent parameters. An explicit formula for the density factor of the MTE is derived. For the example N = 2 we write the MTE in full detail.

Original languageEnglish
Pages (from-to)975-998
Number of pages24
JournalJournal of Physics A: Mathematical and General
Volume36
Issue number4
DOIs
Publication statusPublished - 31 Jan 2003
Externally publishedYes

Fingerprint

Triangular pyramid
Parametrization
tetrahedrons
Fermat Curve
Mathematical operators
operators
Integrable Models
Roots of Unity
Operator
Lattice Model
Explicit Formula
unity
Three-dimensional
curves

Cite this

Von Gehlen, Gunter ; Pakuliak, Stanislav ; Sergeev, S. / Explicit free parametrization of the modified tetrahedron equation. In: Journal of Physics A: Mathematical and General. 2003 ; Vol. 36, No. 4. pp. 975-998.
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Explicit free parametrization of the modified tetrahedron equation. / Von Gehlen, Gunter; Pakuliak, Stanislav; Sergeev, S.

In: Journal of Physics A: Mathematical and General, Vol. 36, No. 4, 31.01.2003, p. 975-998.

Research output: Contribution to journalArticle

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