Geometric Quantization and No Go Theorems

Details Geometric Quantization and No Go Theorems Geometric Quantization and No Go Theorems

1997-03-18

arxiv.org/abs/dg-ga/9703010v1

Mathematics

Differential Geometry

AMS-LaTeX, 10 pages

Scientific paper

A geometric quantization of a K\"{a}hler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist. This is a consequence of a ``no go'' theorem claiming that the entire Lie algebra of smooth functions on a compact symplectic manifold cannot be quantized, i.e., it has no essentially nontrivial finite-dimensional representations.

Affiliated with

Also associated with

No associations

Rating

Geometric Quantization and No Go Theorems 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 Geometric Quantization and No Go Theorems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric Quantization and No Go Theorems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-269653