All Questions
Tagged with qa.quantum-algebra mp.mathematical-physics
17 questions with no upvoted or accepted answers
11
votes
0
answers
264
views
Analogy between BV formalism and integration by residues
Domenico Fiorenza begins his description of the Batalin–Vilkovisky formalism by pointing out an analogy with integration by residues:
Take a top form (density) on $\mathbf R$ resp. space of fields;
...
- 229
9
votes
0
answers
627
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 ...
- 390
7
votes
0
answers
251
views
Is the Dimer Model a TQFT?
The answer to my question is "yes". Technically, it's a spin-TQFT but now I am trying to make sense of that answer.
Dimers on surface graphs and spin structures. I David Cimasoni, Nicolai ...
- 22.8k
7
votes
0
answers
323
views
Flat connection from gauged WZW model
$\newcommand{\g}{\mathfrak g}$
$\newcommand{\h}{\mathfrak h}$
In short my question is :
Has someone worked out the flat connection that one should get from the gauged WZW model in genus 0 ?
Some ...
- 8,524
7
votes
0
answers
182
views
Deformation of Noether's first theorem
Noether's first variational theorem establishes a correspondence between symmetries and invariants. I would like to know what has been written on the following question: How do the invariants deform ...
- 3,880
6
votes
0
answers
578
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 ...
- 61
5
votes
0
answers
103
views
Does this $SU(2)$ Chern-Simons Superconformal Index Example have Modular Properties?
Without any regards to the physics or the geometry used to generate this result, let's examine the formula of Gukov (see p. 32):
$$ \mathcal{I}_{SU(2)}(q,t) = \frac{1}{2}\sum_{m \in \mathbb{Z}}\int \...
- 22.8k
5
votes
0
answers
274
views
Deformation quantization of Poisson bracket without star-product
Kontsevich's formality theorem implies in particular that star-products on a $C^\infty$-manifold $M$,
$$f\star g = fg + \sum_{k\geq1} \hbar^k B_k(f,g),\qquad f,g\in C^\infty(M),$$ where $B_k$ are ...
- 654
5
votes
0
answers
167
views
Distinguishing the Duflo star product
$\newcommand{\g}{\mathfrak g}\newcommand{\h}{\hbar}$
For a finite dimensional Lie algebra $\g$, he Duflo isomorphism is a complicated algebra isomorphism between the $\g$-invariant part $S(\g)^\g$ of ...
- 8,524
5
votes
0
answers
303
views
Quantum dynamics on varieties: asymptotic quantum trace distance on SHL varieties
The Question Asked
Definition: the Second-Hand Lion trace distance $D_k$
Let $\mathcal{M}^{(kk)}_r$ be the set of $k\times k$ complex matrices of rank $\le r$ having unit trace norm. Then the ...
- 1,389
4
votes
0
answers
160
views
Decomposition of the group of Bogoliubov transformations
Consider the fermion Fock space $\mathcal{F}=\bigoplus_{k\ge 0}\bigwedge^k\mathfrak{h}$ of some finite-dimensional 1-particle Hilbert space $\mathfrak{h}$. The group $\mathrm{Bog}(\mathcal{F})$ of ...
- 363
4
votes
0
answers
151
views
Is there a maximal finite depth infinite index irreducible subfactor?
A subfactor $N \subset M $ is irreducible if $N' \cap M = \mathbb{C} $.
It's maximal if it admits no non-trivial intermediate subfactors $N \subset P \subset M $.
It's cyclic if its lattice of ...
4
votes
0
answers
218
views
FRT construction in the case of super algebras
I'm looking on papers which are talking about the super quantum algebra osp(2|1). I want to understand how one applies the FRT construction in the case of osp(2|1).
Of course there is a super ...
- 113
3
votes
0
answers
2k
views
Multiplication of two Pauli string
Given a Pauli string $P_i \in \{ I,X,Y,Z\}^{\otimes n} $
Example: $P_0 = XXYIZ = X \otimes X \otimes Y \otimes I \otimes Z $.
Here $I,X,Y,Z$ are Pauli matrices defined explicitly as:
$$
I = \begin{...
- 131
2
votes
0
answers
193
views
How to write BRST-BV for dg-Lie?
The usual BRST-BV implements a Lie algebra and its module in terms of ghosts, etc.
Where is there written a corresponding formula incorporating the differential of
a dg Lie algebra and module?
- 3,880
2
votes
0
answers
185
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 ...
- 21
0
votes
0
answers
105
views
A variant of quantum harmonic oscillators
We have the following variant of harmonic oscillators.
$$
\left\{
\begin{array}{**lr**}
T = a + a^\dagger\\
a | n \rangle = \sqrt{[n]} |n-1 \rangle \\
a^\dagger |n\rangle = \sqrt{[n+1]} |n+1\...
- 105