38 research outputs found
On Dequantization of Fedosov's Deformation Quantization
To each natural deformation quantization on a Poisson manifold M we associate
a Poisson morphism from the formal neighborhood of the zero section of the
cotangent bundle to M to the formal neighborhood of the diagonal of the product
M x M~, where M~ is a copy of M with the opposite Poisson structure. We call it
dequantization of the natural deformation quantization. Then we "dequantize"
Fedosov's quantization.Comment: 16 pages, latex; references, terminology, notation, and several typos
corrected; to appear in "Letters in Math. Phys.
Formal symplectic groupoid of a deformation quantization
We give a self-contained algebraic description of a formal symplectic
groupoid over a Poisson manifold M. To each natural star product on M we then
associate a canonical formal symplectic groupoid over M. Finally, we construct
a unique formal symplectic groupoid `with separation of variables' over an
arbitrary Kaehler-Poisson manifold.Comment: 41 page, Lemma 13, several typos and notations correcte