Abstract
The exact equations for the spectrum of the finite and infinite quantum Toda chains are derived. The method used does not need the existence of the pseudovacuum (reference) state and provides thus an alter native to the Bethe ansatz method. The results obtained are in good agreement with those of B. Sutherland and M. Gutzwiller.
(Laboratoire associé au CNRS LA 280)
On leave from Steklov Mathematical Institute, Leningrad, USSR.
Preview
Unable to display preview. Download preview PDF.
References
M. Toda — J. Phys. Soc. Ipn. 23, 501 (1967).
M. Toda: Theory of Nonlinear Lattices, Springer (1981).
S.V. Manakov, Zh. Eksp. Teor. Fiz. 67, 543 (1974) Sov. Phys_JETP, 67, 269 (1974)
H. Flaschka, Phys. Rev. B9, 1924 (1974).
H. Flaschka, Progr. Theor. Phys. 51, 703 (1974).
H. Flaschka, D.W. McLaughlin, Progr. Theor. Phys. 55, 438 (1976).
M. Kac, P. Van Moerbeke, Proc. Nat. Acad. Sci. USA, 72, 1627 (1975); ibid. 72, 2879 (1975).
M.A. Olshanetsky, A.M. Perelomov, Lett. Math. Phys. 2, 7 (1977).
B. Sutherland, Rocky Mountain J. Math., 8, 413 (1978).
M.A. Olshanetsky, A.M. Perelomov, Phys. Rep. 71, 313 (1981)
94, 313 (1983).
M.C. Gutzwiller, Ann. Phys., 133, 304 (1981).
L.D. Faddeev, Les Houches Lectures 1982, Elsevier Sci. Publ. (1984).
P.P. Kulish, E.K. Sklyanin, in: Lecture Notes in Physics, 151, 61, Springer (1982).
L.D. Faddeev, Soviet Sci. Rev., Sect. C: Math. Phys. Rev. 1, 107, Harwood Academic, Chur (1980).
V.E. Korepin, Zap. Nauch. Semin. LOMI, 101, 90 (1980) J. Sov. Math. 23, 2429 (1983)
M. Gaudin: La fonction de l'ónde de Bethe pour les modéles exacts de la mécanique statistique, ch. 14, Sur la chaine de Toda, Coll. du Comm. à l'én. at Série sci. (1983).
A.G. Izergin, V.E. Korepin, Comm. Math. Phys., 94, 67 (1984).
V.E. Korepin, Comm. Math. Phys., 94, 93 (1984).
P.P. Kulish, F.A. Smirnov, Phys. Lett., 90A, 74 (1982).
L.D. Faddeev, L.A. Takhtajan, The Hamiltonian Approach to the Soliton Theory, Springer, to be published.
I.V. Komarov, private communication (1983)
A.G. Izergin, V.E. Korepin, Lett. Math. Phys. 8, 259 (1984).
E.K. Sklyanin, Funct. Anal. Appl. 16, 263 (1982); ibid. 17, 273 (1983).
E.K. Sklyanin, Zapiski nauch semin. LOMI, 133, 236 (1984), to be translated in J. Sov. Math..
R.J. Baxter, Ann. Phys. 70, 193 (1972).
N.Yu. Reshetikhin, Lett. Math. Phys. 7, 205 (1983).
C.N. Yang, C.P. Yang, J. Math. Phys. 10, 1115 (1969).
P.M. Morse, H. Feshbach, Methods of Theoretical Physics, v.1, ch. 8, McGraw-Hill (1953).
A. Erdélyi, Higer Transcendental Functions, v.l, McGraw-Hill (1953).
N. Theodorakopoulos, Phys. Rev. Lett. 53, 871 (1984).
I.M. Gelfand, G.E. Shilov: Generalized functions, vol.1, Properties and operations, Academic Press, NY (1964).
N.Yu. Reshetikhin, F.A. Smirnov, Zap. Nauch. Semin. LOMI, 131, 128 (1983) (to be translated in J. Sov. Math.).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag
About this paper
Cite this paper
Sklyanin, E.K. (1985). The quantum Toda chain. In: Sanchez, N. (eds) Non-Linear Equations in Classical and Quantum Field Theory. Lecture Notes in Physics, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15213-X_80
Download citation
DOI: https://doi.org/10.1007/3-540-15213-X_80
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15213-2
Online ISBN: 978-3-540-39352-8
eBook Packages: Springer Book Archive