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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].
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.
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