All Questions
Tagged with quantization reference-request
8 questions
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Is there a version of Nest-Tsygan theorem for smooth variety
Let $M$ be a smooth Poisson manifold and $\mathcal{O}_\hbar (M)$ be a deformation quantisation of $\mathcal{O} (M)$. Nest-Tsygan theorem says that $$HH_i(\mathcal{O}_\hbar (M)[\hbar^{-1}])\cong H^{2d-...
- 367
3
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0
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399
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Bi-differential operators in the definition of star product in deformation quantisation
Let $X$ be an (affine) Poisson variety (not necessarily smooth) over an algebraically closed field of characteristic 0 (such as $\mathbb{C}$), denote $\mathcal{O}(X)$ its ring of functions and $\{-,-\}...
- 367
5
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1
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270
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Is there any work on quantization of distributions?
Let $G$ be a Lie group and consider the space $C_c^\infty(G)$ of compactly supported complex-valued smooth functions on $G$ and $D'(G) = (C_c^\infty(G))'$ the topological dual linear space of $C_c^\...
- 561
6
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3
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Ambidexterity and Quantization
Here the nlab says about Hopkins-Lurie's ambidexterity paper:
"The discussion in the article is apparently motivated as part of what it takes to make precise the discussion of quantization in ...
user62675
3
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2
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531
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Hamiltonian group actions in the context of holomorphic line bundles
When studying Hamiltonian group actions, a very nice set up might be to take the following:
Let $M$ be a compact Kähler manifold with (integral) Kähler form $\omega$, endowed with a Hamiltonian $G$ ...
- 627
3
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1
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161
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Reference of $\hbar$-differential operator from symplectic geometry perspective
I am reading Bates and Weinstein's book 'Lectures on the Geometry of Quantization'. In Chapter 6, they defined the $\hbar$-differential operator, and showed (Theorem 6.7) that the Lagrangian ...
- 587
6
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3
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265
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graded generalization of the Moyal–Weyl product
Has anyone written about the graded generalization of the Moyal–Weyl product/star product, that is, where the original algebra is already graded? Is it just a matter of signs?
- 3,880
7
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7
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Quantization of a classical system (e.g. the case of a billiard)
There have been already several questions asking for an introduction to quantum mechanics
for a mathematician, but this one is slightly different, and more restrictive.
I know (some)
quantum ...
- 26.1k