Mathematics – Symplectic Geometry
Scientific paper
2011-03-08
Mathematics
Symplectic Geometry
Lecture Notes, International School on Geometry and Quantization, University of Luxembourg, August 31 - September 5, 2009, 37
Scientific paper
In the presence of classical phase space singularities the standard methods are insufficient to attack the problem of quantization.In certain situations the difficulties can be overcome by means of K\"ahler quantization on stratified K\"ahler spaces. Such a space is a stratified symplectic space together with a complex analytic structure which is compatible with the stratified symplectic structure; in particular each stratum is a K\"ahler manifold in an obvious fashion. Holomorphic quantization on a stratified K\"ahler space then yields a costratified Hilbert space, a quantum object having the classical singularities as its shadow. Given a K\"ahler manifold with a hamiltonian action of a compact Lie group that also preserves the complex structure, reduction after quantization coincides with quantization after reduction in the sense that not only the reduced and unreduced quantum phase spaces correspond but the invariant unreduced and reduced quantum observables as well
Huebschmann Johannes
Lille U.
No associations
LandOfFree
Singular Poisson-Kähler geometry of stratified Kähler spaces and quantization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Singular Poisson-Kähler geometry of stratified Kähler spaces and quantization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Singular Poisson-Kähler geometry of stratified Kähler spaces and quantization will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-83027