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Results tagged with ag.algebraic-geometry
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user 12482
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
8
votes
Accepted
Some elementary questions about deformation quantization
a lot of questions, let me try on some of them :)
The bad news is that in most of the interesting situations the higher order terms of the star product, the $B_i$ will not vanish. Heuristically this …
- 8,098
3
votes
Reverse Engineering to find deformation problem (from cohomology groups)?
In this generality, I would say that this is not possible: the same cohomology can be responsible for controlling quite different deformations problems.
Just an example: in formal deformation quantiz …
- 8,098
3
votes
Can you tell the volume of a symplectic manifold from the Poisson brackets?
Let me add a few remarks on Theo's answer. For a compact connected symplectic manifold, it is known that the integration with respect to the Liouville volume form (whatever normaliyation you prefer) i …
- 8,098
8
votes
When (why) did we allow manifolds to be non-Hausdorff and/or non-second countable?
Non-Hausdorffness shows up in several contexts when dealing with Lie groupoids: the integration (Lie's 3rd Theorem) for Lie algebroids to Lie groupoids will typically produce a non-Hausdorff one, if i …
- 8,098
2
votes
Quantum Grassmannians?
There is a deformation quantization approach to the quantization of the Grassmannians taking their Kähler symplectic form as the starting point. You can find this in the preprint by Schirmer arXiv:q-a …
- 8,098
4
votes
Accepted
Prequantization and Hilbert space
OK, so here are just a few thought on this large topic of quantization. First of all, the question of irreducibility can equally well be asked for deformation quantization (as mentioned by other answe …
- 8,098
18
votes
Clifford algebras as deformations of exterior algebras
In addition to the answer of Bertram Arnold, let me point out that there is a very explicit formula for "fermionic" Weyl-Moyal product. Let us assume that your vector space $V$ (or module) is defined …
- 8,098