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Results tagged with mp.mathematical-physics
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user 12482
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
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 …
- 8,098
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 …
- 8,098
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 …
- 8,098
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 …
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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 …
- 8,098
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 …
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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 …
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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 …
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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 …
- 8,098
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 …
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