From geometric quantization to Moyal quantization

Weyl Quantization from Geometric Quantization

In [23] a nice looking formula is conjectured for a deformed product of functions on a symplectic manifold in case it concerns a hermitian symmetric space of non-compact type. We derive such a formula for simply connected symmetric symplectic spaces using ideas from geometric quantization and prequantization of symplectic groupoids. We compute the result explicitly for the natural 2-dimensional...

Moyal quantization of necklace Lie algebras

We use Moyal-type formulas to construct a Hopf algebra quantization of the necklace Lie bialgebra associated with a quiver.

Branes from Moyal Deformation Quantization of Generalized Yang Mills Theories

It is shown that a Moyal deformation quantization of the SO(4k) Generalized Yang-Mills (GYM) theory action in D = 4k dimensions, for spacetime independent field configurations, in the h̄ → 0 limit, yields the Dolan-Tchrakian p-brane action after fixing the conformal and world volume reparametrization invariance , associated with the p-brane world volume dimension p + 1 = 4k, embedded in a D = 4k...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

Geometric Quantization from a Coherent State Viewpoint

A fully geometric procedure of quantization that utilizes a natural and necessary metric on phase space is reviewed and briefly related to the goals of the program of geometric quantization. Introduction and Background Purpose and achievements The goal of the present work is to present a conceptually simple, geometric prescription for quantization. Such a goal has been, and continues to be, the...