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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.
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
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
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
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
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
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