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On Weyl Quantization from geometric Quantization

P. de M. Rios·G. M. Tuynman
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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.

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P. de M. Rios, G. M. Tuynman. 2002-03-12. On Weyl Quantization from geometric Quantization. https://doi.org/10.1063/1.3043868

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