Abstract
It is shown how the classical trigonometric τ-matrices of the Toda model can be obtained by a Hamiltonian reduction of the cotangent bundle over loop groups.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. A. Belavin and V. G. Drinf’eld,Funkts. Anal. Prilozhen.,16, No. 3, 1–29 (1982).
M. Jimbo, “Springer lectures in physics,” in:Current Topics in QFT. Seminar Proceedings, Springer, Berlin (1985), p. 35–62.
M. A. Olshanetsky and A. M. Perelomov,Invent. Math.,37, 93 (1976).
L. Ferreira and D. Olive,Commun. Math. Phys.,99, 365–384 (1985).
J. Avan, O. Babelon, and M. Talon,Algebra Anal.,6, No. 2, 67–89 (1994).
L. A. Takhtajan and L. D. Faddeev,The Hamiltonian Methods in the Theory of Solitons, Berlin-Heidelberg-New York, Springer (1987).
V. Kac,Infinite Dimensional Lie Algebras, Cambridge Univ., Cambridge (1993).
A. Pressley and G. Segal,Loop Groups, Clarendon, Oxford (1986).
V. I. Arnold,Mathematical Methods of Classical Mechanics, Springer, Berlin-New York (1989).
O. I. Bogoyavlensky,Commun. Math. Phys.,51, 201–209 (1976).
Author information
Authors and Affiliations
Additional information
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 3–12, October, 1997.
Rights and permissions
About this article
Cite this article
Arutyunov, G.E. Construction of trigonometric Todar-matrices via a hamiltonian reduction of the cotangent bundle over loop groups. Theor Math Phys 113, 1209–1216 (1997). https://doi.org/10.1007/BF02634008
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02634008