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# Questions tagged [quantization]

Questions on various methods and aspects of quantization

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0 votes
2 answers
213 views

• 151
1 vote
0 answers
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### Problem in understanding Theorem $6.2.9$ from Chari and Pressley

The theorem I am referring to here says that if we start with a Lie bialgebra $\mathfrak g$ determined by some skew-symmetric element $r \in \mathfrak g \otimes \mathfrak g$ satisfying classical Yang-...
• 189
3 votes
1 answer
205 views

### Understanding definition of quantization of a Poisson-Hopf algebra

I am going through the chapter Quantization of Lie bialgebras from the book A Guide to Quantum Groups by Chari and Pressley. There I found a notion called Quantization which deals with deformations of ...
• 189
9 votes
2 answers
533 views

• 367
3 votes
0 answers
363 views

• 8,707
5 votes
1 answer
254 views

• 1,619
8 votes
1 answer
418 views

• 654
9 votes
1 answer
356 views

### Geometric quantization: why are the prequantum operators self-adjoint?

I'm reading a bit about geometric quantization and, among the axioms of this construction, is one requiring that the operator $\hat f = -\textrm i \hbar \nabla _{X_f} + f$ associated to the classical ...
• 5,282
5 votes
0 answers
165 views

### Distinguishing the Duflo star product

$\newcommand{\g}{\mathfrak g}\newcommand{\h}{\hbar}$ For a finite dimensional Lie algebra $\g$, he Duflo isomorphism is a complicated algebra isomorphism between the $\g$-invariant part $S(\g)^\g$ of ...
• 8,369
4 votes
0 answers
319 views

### Quantization of $S^2$ as $C^*$-algebra?

The general context for the question - is belief that quantization of compact symplectic manifolds can be endowed with the structure of $C^*$-algebra (see MO230695). The particular question is about ...
9 votes
0 answers
256 views

### Existence/characterization/properties of $C^*$-algebras which "are" quantization of compact symplectic manifolds?

Understanding of "quantization" achieved much progress recent years, especially after Kontsevich breakthrough on deformation quantization, where he proved one-to-one correspondence between Poisson ...
15 votes
0 answers
459 views

### Squeezing physics out of formal deformation quantizations

I am reading various texts concerning the concept of "quantization". I am interested in quantization on Riemannian manifolds (as opposed to just on $\Bbb R ^n$); for absolute clarity, I am interested ...
• 5,282
35 votes
5 answers
5k views

### Does quantum mechanics ever really quantize classical mechanics?

I was curious about a physics question which I thought might be suitable for mathoverflow. I looked at the answer to this question, but it's not what I'm looking for. Basically, classical mechanics ...
• 7,902
3 votes
0 answers
393 views

### From symplectic manifold to Hilbert spaces [closed]

What could be a mathematical model of such physical wish? I'm looking for something sending a symplectic manifold $(M,\omega)$ to a Hilbert space $H_{M}$ with the following properties: 1- We should ...
• 1,607
6 votes
3 answers
2k views

### 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 ...
3 votes
2 answers
487 views

### 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 votes
1 answer
159 views

### 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 ...
• 577
6 votes
1 answer
388 views

### The function algebra $C^{\infty}(M\#N)$ of the connected sum of two spaces

Operations such as taking union or Cartesian products of spaces have direct analogues in term of algebra of functions on them (direct sum and tensor product, respectively), my question is: Is there ...
• 309