All Questions
9 questions
71
votes
10
answers
11k
views
The Planck constant for mathematicians
The questions
Q1. What are simple ways to think mathematically about the physical meanings of the Planck constant?
Q2. How does the Planck constant appear in mathematics of quantum mechanics? In ...
- 24.7k
9
votes
0
answers
544
views
From classical to quantum mechanics
Let ($X,\omega$) be a symplectic manifold (phase space of some physical system). Consider the algebra $\mathcal{C}^{\infty}(X,\mathbb{R})$ of smooth functions on $X$ and $[\omega]\in \textrm{H}^{2}_{\...
- 1,629
15
votes
0
answers
472
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 ...
- 5,407
3
votes
0
answers
413
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
265
views
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
13
votes
1
answer
678
views
Reconciling two notions of geometric quantization.
Let $(M,\omega)$ be a compact symplectic manifold and $(L,\nabla)$ a prequantum line bundle. There are two schemes to quantize this data:
Choose a polarization $P$ of $M$ and define the quantum ...
- 3,244
7
votes
7
answers
2k
views
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
10
votes
1
answer
2k
views
basic questions on quantum integrable systems
I have been learning about (classical) integrable systems lately, e.g. in the examples of a Lax pair etc. I frequently run into the term 'quantum integrable system'. May I ask a few questions:
What ...
- 1,719
-1
votes
2
answers
684
views
Problem of quantization: state of the art
The "problem of quantization":
Find a vector space $Obs$ (as large as possible) of real-valued functions $f(p, q)$ on $R^{2n}$, containing the coordinate ...
- 279