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Asymptotic and geometric quantization. (English. Russian original) Zbl 0588.58031
Russ. Math. Surv. 39, No. 6, 133-205 (1984); translation from Usp. Mat. Nauk 39, No. 6(240), 115-173 (1984).
In their survey the authors deal with the connection between geometric quantization and deformations of Poisson brackets and the theory of pseudodifferential operators. They develop a calculus of pseudodifferential operators with symbols on general symplectic manifolds and calculate the spectral series of nearly integrable Hamiltonian systems.
Reviewer: N.Jacob

MSC:
53D50 Geometric quantization
35S05 Pseudodifferential operators as generalizations of partial differential operators
81S99 General quantum mechanics and problems of quantization
58J40 Pseudodifferential and Fourier integral operators on manifolds
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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