# Tagged Questions

**4**

votes

**0**answers

146 views

### Quantum Drinfeld-Sokolov reduction for a module

There is a well-established procedure for quantizing the Drinfeld-Sokolov reduction for an affine Lie algebra. In particular, this paper of de Boer and Tjin describes an algorithm to produce the ...

**6**

votes

**1**answer

273 views

### Are Turaev--Viro invariants secretly a discretized path integral?

Turaev--Viro http://www.ams.org/mathscinet-getitem?mr=1191386 defined an invariant of three-manifolds $M$ denoted $TV(M)$, which was subsequently shown by Kevin Walker to coincide with ...

**4**

votes

**0**answers

103 views

### Is there a maximal finite depth infinite index irreducible subfactor?

A subfactor $N \subset M $ is irreducible if $N' \cap M = \mathbb{C} $.
It's maximal if it admits no non-trivial intermediate subfactors $N \subset P \subset M $.
It's cyclic if its lattice of ...

**7**

votes

**1**answer

1k views

### The cyclic subfactors theory: a quantum arithmetic?

Context: First recall some results:
- Actions of finite groups on the hyperfinite type $II_{1}$ factor $R$ (Jones 1980).
- A Galois correspondence for depth 2 irreducible subfactors ...

**13**

votes

**2**answers

891 views

+50

### What is quantum Brownian motion?

It seems that the current state of quantum Brownian motion is ill-defined. The best survey I can find is this one by László Erdös, but the closest the quantum Brownian motion comes to appearing is in ...

**8**

votes

**2**answers

416 views

### Is the quantum algebra unique (up to isomorphism) in deformation quantization ?

Consider a Poisson algebra A (i.e. commutative algebra with Poisson bracket).
Let $\hat A$ be a deformation quantization of the algebra A. We know that construction of deformation quantization and ...

**4**

votes

**0**answers

113 views

### FRT construction in the case of super algebras

I'm looking on papers which are talking about the super quantum algebra osp(2|1). I want to understand how one applies the FRT construction in the case of osp(2|1).
Of course there is a super ...

**4**

votes

**0**answers

368 views

### Jones Polynomial and Quantum Field Theory

I am trying Witten's paper but unable to re-produce the computations presented in the paper.
I tried few things on internet but all these tutorials explicitly don't show the calculations and refer to ...

**6**

votes

**4**answers

455 views

### level 2,3 characters of affine su(2)

Does anyone know where I can find an explicit formula to compute the level 2 or level 3
characters of affine $su(2)$? I have found several sources that give a formula to compute the
level 1 ...

**1**

vote

**0**answers

136 views

### quantization of Poisson manifolds/ bialgebras

Can we apply the theorem of quantization of Lie bialgebras of Etingof-Kazdhan http://www.springerlink.com/content/h285401597138rg7/ to a Poisson manifold $\textbf{R}^{n}?$
Does it give something in ...

**5**

votes

**0**answers

253 views

### Quantum dynamics on varieties: asymptotic quantum trace distance on SHL varieties

The Question Asked
Definition: the Second-Hand Lion trace distance $D_k$
Let $\mathcal{M}^{(kk)}_r$ be the set of $k\times k$ complex matrices of rank $\le r$ having unit trace norm. Then the ...

**-4**

votes

**1**answer

2k views

### Quantum dynamics on varieties and Salmon Prizes

Concluding Progressive Remarks
A new finding is Bates and Oeding's preprint "Toward a salmon conjecture" (arXiv:1009.6181), with its reference to the Salmon Prize.
The Salmon Prize (photo of the ...

**7**

votes

**1**answer

639 views

### Coherent states vs quantization of Lagrangian submanifold

Coherent states http://en.wikipedia.org/wiki/Coherent_states
are vectors in the Hilbert space which in certain sense are strongly localized
and "corresponds" to points in classical phase space (see ...

**3**

votes

**3**answers

318 views

### Open symplectic embeddings and deformation quantization

I would like to know whether there is a specific relationship between the deformation quantizations of the Poisson algebras of the functions on a symplectic manifold, say $M$, and of the functions on ...

**4**

votes

**1**answer

352 views

### What is known rigoruously about the semiclassical (k to infinity) limit of WRT invariants?

To each closed $3$-manifold $N$, there is a corresponding Witten--Reshetikhin--Turaev invariant $Z_k(N)$ depending on an integer $k$ (the level) and a Lie group $G$ (and perhaps we'll just concentrate ...

**22**

votes

**3**answers

2k views

### Why is a 2d TQFT formulated as a functor?

Usual mathematical formulation of a 2d (closed) TQFT is as a functor from the category of 2-dim cobordisms between 1-dim manifolds to the category of vector spaces (satisfying various properties.)
...

**6**

votes

**2**answers

2k views

### Non-degeneracy of ground state in quantum mechanics

In non-relativistic quantum mechanics, what are the necessary conditions on the potential (or on the hamiltonian in general) for the ground state to be non-degenrate?

**4**

votes

**1**answer

505 views

### The bosonic and fermionic parts of the orthosymplectic super Lie-Algebra

To phrase the question in a concrete way, I read in a paper:
The super Poincare subalgebra of osp(6,2|4) has bosonic part $so(5,1) \oplus usp(4) \simeq so(5,1) \oplus so(5)$.
It's hard to unpack ...

**9**

votes

**1**answer

898 views

### Spectral theory for self-adjoint field operators on a symmetric Fock space

Background
Suppose we have a finite-dimensional Hilbert space $H = \mathbb{C}^s$ (for a natural number s) and we construct the symmetric (or bosonic) Fock space built from it: $$F(H):= \mathbb{C} ...

**0**

votes

**2**answers

820 views

### Quantum channels, question 2: tensor products and composition of functions

Please be kind. I've been working on this for a long time and can't find an answer. Feel free to edit for clarity if you think the question can be better worded.
Background
It may help to see a ...

**32**

votes

**6**answers

5k views

### The 'real' use of Quantum Algebra, Non-commutative Geometry, Representation Theory, and Algebraic Geometry to Physics

In this question, Orbicular made the following comment to Feb7 and my own answers;
Please keep in mind that - even though it is stated very often - noncommutative geometry does not give "real" ...

**5**

votes

**4**answers

618 views

### Quantum channels as categories: question 1.

A quantum channel is a mapping between Hilbert spaces, $\Phi : L(\mathcal{H}_{A}) \to L(\mathcal{H}_{B})$, where $L(\mathcal{H}_{i})$ is the family of operators on $\mathcal{H}_{i}$. In general, we ...

**4**

votes

**2**answers

580 views

### Categorifications of the Fibonacci Fusion Ring arising from Conformal Field Theory

I was reading about realizations of the "Fibonacci" fusion ring $X \otimes X = X \oplus 1$ in Fusion Categories of Rank 2 by Victor Ostrik. Apparently, there are two of them and they arise in various ...

**41**

votes

**11**answers

4k views

### What is Quantization ?

I would like to know what quantization is, I mean I would like to have some elementary examples, some soft nontechnical definition, some explanation about what do mathematicians quantize?, can we ...