Karasëv, M. V.; Maslov, V. P. 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 Cited in 6 ReviewsCited in 33 Documents 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 Keywords:pseudodifferential operators with symbols on a symplectic manifold; nearly integrable Hamiltonian systems; geometric quantization PDFBibTeX XMLCite \textit{M. V. Karasëv} and \textit{V. P. Maslov}, Russ. Math. Surv. 39, No. 6, 133--205 (1984; Zbl 0588.58031); translation from Usp. Mat. Nauk 39, No. 6(240), 115--173 (1984) Full Text: DOI