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Questions on various methods and aspects of quantization

10 votes
Accepted

Quantization by cohomology

The case can be made that all of quantization is via cohomology, namely that quantization is fundamentally pull-push in some generalized cohomology theory, hence is index theory. … Type-semantics for quantization it is observed that at the heart of it cohomological quantization is a fundamental operation in Grothendieck's "yoga of six functors". …
Urs Schreiber's user avatar
5 votes
Accepted

Physical meaning of the integral cohomology condition in Souriau-Kostant pre-quantization?

This is spelled out in a good bit of detail in the nLab entry geometric quantization of the 2-sphere. … So one may wonder if maybe at a deeper leverl the cohomological condition that plays a role - for instance in more general situations not covered by traditional geometric quantization, such as the quantization
Urs Schreiber's user avatar
5 votes
Accepted

Reconciling two notions of geometric quantization.

Klaas Landsman has been proposing that geometric quantization is best understood as taking values in KK-cocycles. … From this and various other perspectives it looks like regarding geometric quantization as a map into KK-theory is a rather attractive idea. …
Urs Schreiber's user avatar