Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 12482

Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

18 votes

Applications of symplectic geometry to classical mechanics

The list will be long, very long indeed. But to start: Questions about dynamics of Hamiltonian systems are at the heart of symplectic topology, symplectic capacities are precisely introduced for that …
Stefan Waldmann's user avatar
78 votes

The Planck constant for mathematicians

Let's give it a try. Of course, the precise mathematical meaning is perhaps absent, so the answers are sort of heuristic. But if I understand correctly, you want to gain intuition ;) The first observ …
Stefan Waldmann's user avatar
4 votes

Deformation quantization of a closed Riemann surface with genus >1

One should definitely take a look at the work of Bordemann, Meinrenken, and Schlichenmaier: they provide a Berezin-Toeplitz inspired deformation quantization for all compact quantizable (i.e. the Kähl …
Stefan Waldmann's user avatar
3 votes

graded generalization of the Moyal–Weyl product

Yes, it's just putting signs correctly. Martin Bordemann has a preprint from the 90s where he adapted Fedosov's construction in the graded setting. If you are only interested in the flat situation thi …
Stefan Waldmann's user avatar
6 votes
Accepted

Formal series convergence in deformation quantization and $C^*$-condition

OK, let me give a try on this question. There are several problems hidden underneath which one has to address. First, for physical reasons a formal deformation is not sufficient. $\hbar$ is a constan …
Stefan Waldmann's user avatar
13 votes

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

In deformation quantization there is a full classification available: let us first focus on the symplectic case which is easier. If $(M, \omega)$ is a symplectic manifold (like the $\mathbb{R}^2$ in y …
Stefan Waldmann's user avatar
17 votes
Accepted

Can a sphere be a phase space?

Of course, the spheres are compact while cotangent bundles are noncompact (unless in dimension 0). Nevertheless, a bit more interesting is the question whether the even dimensional spheres can be phas …
Stefan Waldmann's user avatar
4 votes
Accepted

Open symplectic embeddings and deformation quantization

Hi Igor, there is a quite elementary way to see that star products restrict to open subsets: it's essentially part of the definition of a star product. Here, I will focus on the case of smooth (sympl …
Stefan Waldmann's user avatar
9 votes

Dimensional Analysis in Mathematics

Dimensional analysis can be viewed as the study of graded objects in algebra. The grading then corresponds to "counting the units" in a precise way. There are of course many examples and I believe tha …
Stefan Waldmann's user avatar
28 votes
Accepted

Quantum mechanics formalism and C*-algebras

In addition to what has already been said I would like to add some more comments. I completely understand your suspicion that the passage from unbounded operators to bounded ones is at least tricky. F …
Stefan Waldmann's user avatar