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3
votes
0answers
18 views

Second order term of the Fedosov quantised product

In Fedosov's version of quantisation of functions on a symplectic manifold, the product is given in terms of a symplectic connection. I have looked through Fedosov's book in deformation quantisation, ...
1
vote
0answers
63 views

The normalization axiom of a quantization

Guillemin, Ginzburg and Karshon explain a quantization in their book [Chap 6,MR1929136] as follows. The quantization is a process which associates to a symplectic manifold $M$ a Hilbert space ...
3
votes
0answers
173 views

Why is geometric quantization (esp. Berezin-Toeplitz quantization) interesting for a symplectic geometer/topologist?

I know that many symplectic geometers are interested in quantization as well. From what I understood, quantization isn't expected to be used as a tool to answer symplectic questions (as in ...
2
votes
0answers
80 views

Complex structure on the set of prequantization line bundles

For geometric quantization, the set of equivalence classes of prequantization line bundles of a quantizable symplectic manifold $(M, ω)$ is parametrized by $H^1(M, S^1)$ which represents the ...
1
vote
1answer
343 views

pre-quantization of Jet bundle

We know that the notion of Jet bundle $J^kM×\mathbb{R}$, is generalization of cotangent bundle. What is the prequantization of $J^kM×\mathbb{R}$?
2
votes
1answer
360 views

a question about geometric quantization background

I don't understand why for geometric description of a regular system, we take always the classical phase space as a symplectic manifold?