×
Vorob’ev, Yu. M.; Dobrokhotov, S. Yu.

Quasiclassical quantization of the periodic Toda chain from the point of view of Lie algebras. (English. Russian original) Zbl 0517.58023

Theor. Math. Phys. 54, 312-314 (1983); translation from Teor. Mat. Fiz. 54, No. 3, 477-480 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0517.58023

Cited in 2 Documents

MSC:

53D50 Geometric quantization
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis

Keywords:

asymptotic representation; quantum periodic Toda chain; Hamilton operator; Maslov method
Cite Review PDF
Full Text: DOI

References:

[1] S. Yu. Dobrokhotov and V. P. Maslov, in: Modern Problems of Mathematics, Vol. 15 (Itogi Nauki i Tekhn. VINITI AN SSSR) [in Russian], VINITI, Moscow (1980).
[2] I. M. Krichever, Usp. Mat. Nauk,33, 215 (1978).
[3] H. Flaschka and D. W. McLaughlin, Prog. Theor. Phys.,55, 438 (1976). · Zbl 1109.35374 · doi:10.1143/PTP.55.438
[4] B. A. Dubrovin, V. B. Matveev, and S. P. Novikov, Usp. Mat. Nauk,31, 55 (1976).
[5] L. D. Faddeev, ?Quantum completely integrable field theory models,? Preprint LOMI R-2-79 [in Russian], Leningrad Branch, V. A. Steklov Mathematics Institute, Leningrad (1979).
[6] M. V. Karasev and V. P. Maslov, in: Modern Problems of Mathematics, Vol. 13 (Itogi Nauki i Tekhn. VINITI AN SSSR) [in Russian], VINITI, Moscow (1979).
[7] M. V. Karasev, Teor. Mat. Fiz.,31, 41 (1977).
[8] V. P. Maslov, Operator Methods [in Russian], Nauka, Moscow (1973).
[9] A. A. Kirillov, Elements of the Theory of Representations [in Russian], Nauka, Moscow (1972). · Zbl 0249.22012
[10] V. P. Maslov and M. V. Fedoryuk, Quasiclassical Approximation for the Equations of Quantum Mechanics [in Russian], Nauka, Moscow (1976). · Zbl 0449.58002
[11] M. V. Karasev, ?V. P. Maslov’s quantization conditions in higher cohomologies and analogs of the entities of Lie’s theory for canonical fibrations of symplectic manifolds,? Deposited Paper No. 1092-82, VINITI (1982).
[12] B. A. Dubrovin, Usp. Mat. Nauk.,36, 72 (1981).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.