Elliptic Algebra and Integrable Models for Solitons on Noncummutative Torus $\mathcal{T}$

Abstract

We study the algebra ${\mathcal{A}}_n$ and the basis of the Hilbert space ${\mathcal{H}}_n$ in terms of the $\theta$ functions of the positions of $n$ solitons. Then we embed the Heisenberg group as the quantum operator factors in the representation of the transfer matrice of various integrable models. Finally we generalize our result to the generic $\theta$ case.

Talk given by Bo-Yu Hou at the Joint APCTP-Nankai Symposium. Tianjin (PRC), Oct. 2001. To appear in the proceedings, to be published by Int. J. Mod. Phys. B. 7 pages, latex, no figures

References in corpus (13)

• String Theory and Noncommutative Geometry
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Noncommutative Solitons
• Gaudin Model, Bethe Ansatz and Critical Level
• Komaba Lectures on Noncommutative Solitons and D-Branes
• Noncommutative Tachyons And String Field Theory
• Exact Noncommutative Solitons
• Noncommutative Solitons on Orbifolds
• Exact solitons on noncommutative tori
• Solitons on compact and noncompact spaces in large noncommutativity
• Exact Tachyon Condensation on Noncommutative Torus
• Elliptic Ruijsenaars-Schneider and Calogero-Moser Models Represented by Sklyanin Algebra and sl(n) Gaudin Algebra
• Solitons on Noncommutative Torus as Elliptic Algebras and Elliptic Models

Cited by in corpus (2)

• Soliton Solutions on Noncommutative Orbifold $ T^2/Z_4
• The manifest covariant soliton solutions on noncommutative orbifold $T^2/Z_6$ and $T^2/Z_3$