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

Physics – High Energy Physics – High Energy Physics - Theory

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Talk given by Bo-Yu Hou at the Joint APCTP-Nankai Symposium. Tianjin (PRC), Oct. 2001. To appear in the proceedings, to be pub

Scientific paper

10.1142/S0217979202011822

We study the algebra ${\cal A}_n$ and the basis of the Hilbert space ${\cal
H}_n$ 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.

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