English

On Weyl Quantization from geometric Quantization

Mathematical Physics 2015-06-26 v2 math.MP Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.math-ph/0201044,
  title  = {On Weyl Quantization from geometric Quantization},
  author = {P. de M. Rios and G. M. Tuynman},
  journal= {arXiv preprint arXiv:math-ph/0201044},
  year   = {2015}
}

Comments

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