11
votes
Physical intuition behind prequantization spaces
If you think instead of the prequantum line bundle (i.e. the complex line bundle associated to your prequantum circle bundle using the standard representation of the circle on $\mathbb{C}$) then the ...
- 7,005
7
votes
Accepted
Fedosov vs. Kontsevich deformation quantization : a beginner survey
Fedosov's work seems to be also available with details in a book Deformation quantization and index theory. Are the two references overlapping ?
Yes, indeed. The book contains strictly more than the ...
- 8,385
3
votes
Accepted
Hilbert module over $C_0(\Lambda)$ as space of continuous sections of HIlbert bundle
The reference I cited in my book is Fell and Doran, Representations of ${}^*$-Algebras, Locally Compact Groups, and Banach ${}^*$-Algebraic Bundles, vol. 1 (1988). Did you check there? I don't have a ...
- 42.8k
2
votes
Accepted
Does symplectic morphism after geometric quantization induce Hilbert spaces morphism?
The slogan to keep in mind is that "quantization is not a functor". For details on this slogan, see the (decade old!) Mathoverflow question What does “quantization is not a functor” really mean?. ...
- 54.6k
1
vote
Inner product on global sections of positive line bundle
This is in general false, if I am not missing anything. Suppose you start from the form $\Omega_0$ given by the Chern connection on $O(1)$ with respect to the standard metric coming from $\mathbb{C}^...
- 11
1
vote
On the existence and classification of prequantization spaces over a closed symplectic manifold
There exists an exact sequence $0\rightarrow \mathbb{Z}\rightarrow\mathbb{C}\rightarrow\mathbb{C}^*\rightarrow 1$ defined by the expontial map which induces an isomorphism $H^2(M,\mathbb{Z})\...
- 3,652
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