๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the deformation quantization of symplectic orbispaces

โœ Scribed by Markus J. Pflaum

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
335 KB
Volume
19
Category
Article
ISSN
0926-2245

No coin nor oath required. For personal study only.

โœฆ Synopsis

In the first part of this article we provide a geometrically oriented approach to the theory of orbispaces originally introduced by G. Schwarz and W. Chen. We explain the notion of a vector orbibundle and characterize the good sections of a reduced vector orbibundle as the smooth stratified sections. In the second part of the article we elaborate on the quantizability of a symplectic orbispace. By adapting Fedosov's method to the orbispace setting we show that every symplectic orbispace has a deformation quantization. As a byproduct we obtain that every symplectic orbifold possesses a star product.

๐Ÿ“œ SIMILAR VOLUMES

On the geometric quantization of the sym
On the geometric quantization of the symplectic leaves of Poisson manifolds
โœ Izu Vaisman ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 861 KB

In the paper, we establish some conditions which ensure one of the following: (i) the existence of the pullback of the quantization bundle of a Poisson manifold to a quantization bundle of a symplectic leaf, (ii) the existence of the projection of a quantization bundle from a presymplectic realizati

Field theory on the q-deformed fuzzy sph
Field theory on the q-deformed fuzzy sphere II: quantization
โœ H. Grosse; J. Madore; H. Steinacker ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 292 KB

We study the second quantization of field theory on the q-deformed fuzzy sphere for q โˆˆ R. This is performed using a path integral over the modes, which generate a quasi-associative algebra. The resulting models have a manifest U q (su( 2)) symmetry with a smooth limit q โ†’ 1, and satisfy positivity