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https://doi.org/10.1063/1.3043...
Article . 2008 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2002
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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Weyl Quantization from geometric quantization

Authors: P. de M. Rios; G. M. Tuynman; Piotr Kielanowski; Anatol Odzijewicz; Martin Schlichenmaier; Theodore Voronov;

Weyl Quantization from geometric quantization

Abstract

A. Weinstein has conjectured a nice looking formula for a deformed product of functions on a hermitian symmetric space of non-compact type. We derive such a formula for symmetric symplectic spaces using ideas from geometric quantization and prequantization of symplectic groupoids. We compute the result explicitly for the natural 2-dimensional symplectic manifolds: the euclidean plane, the sphere and the hyperbolic plane. For the euclidean plane we obtain the well known Moyal-Weyl product. The other cases show that Weinstein's original idea should be interpreted with care. We conclude with comments on the status of our result.

11 pages. (v2: corrected a couple of typos)

Related Organizations
Keywords

53c35, 53d50, 53d55, 53z05, Mathematics - Symplectic Geometry, FOS: Mathematics, Symplectic Geometry (math.SG), FOS: Physical sciences, Mathematical Physics (math-ph), Mathematical Physics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green