%0 Journal Article
%T On Weyl Quantization from geometric Quantization
%A P. de M. Rios
%A G. M. Tuynman
%J Mathematics
%D 2002
%I arXiv
%R 10.1063/1.3043868
%X 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.
%U http://arxiv.org/abs/math-ph/0201044v2