Nazaikinskij, Vladimir; Sternin, Boris Wave packet transform in symplectic geometry and asymptotic quantization. (English) Zbl 0915.58108 Komrakov, B. P. (ed.) et al., Lie groups and Lie algebras. Their representations, generalisations and applications. Dordrecht: Kluwer Academic Publishers. Math. Appl., Dordr. 433, 47-69 (1998). A quantization procedure based on an integral transformation called wave packet transform is proposed. This is an invertible mapping of the space of functions on the configuration space to a subspace of the functions on the phase space. The considered mapping is closely related to the Bargmann transform. It is shown that the proposed quantization procedure coincides in the leading term with the Schrödinger quantization and with Maslov quantization for Lagrangian modules.For the entire collection see [Zbl 0886.00009]. Reviewer: Dmitry Kalinin (Kazan’) MSC: 58Z05 Applications of global analysis to the sciences 83C57 Black holes 53B30 Local differential geometry of Lorentz metrics, indefinite metrics 83C75 Space-time singularities, cosmic censorship, etc. Keywords:quantization; Bargmann transform; Maslov canonical operator; anti-Wick symbol PDFBibTeX XMLCite \textit{V. Nazaikinskij} and \textit{B. Sternin}, Math. Appl., Dordr. 433, 47--69 (1998; Zbl 0915.58108)