
arXiv: math-ph/0201044
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)
53c35, 53d50, 53d55, 53z05, Mathematics - Symplectic Geometry, FOS: Mathematics, Symplectic Geometry (math.SG), FOS: Physical sciences, Mathematical Physics (math-ph), Mathematical Physics
53c35, 53d50, 53d55, 53z05, Mathematics - Symplectic Geometry, FOS: Mathematics, Symplectic Geometry (math.SG), FOS: Physical sciences, Mathematical Physics (math-ph), Mathematical Physics
| 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). | 1 | |
| 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. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
