Talk:Symplectomorphism
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QM edit
Heh. I just learned something today, which I think is utterly fascinating. Turns out the quantum-mechanical Schroedinger equation is nothing more (and nothing less!) than a purely classical Hamiltonian flow on CP^n. Heh! Here, a quantum mechanical state is regarded as a point in CP^n, i.e. a point on the Bloch sphere. Hamiltonian flows can be defined only if there is a symplectic form on the manifold... but of course, CP^n has the Fubini-Study metric, and so has the requisite symplectic form! Golly! This does have this forehead-slapping, "but of course, what else could it be" element to it, but .. well, I'm tickled. I'll have to work some sample problems in this new-found language. linas 04:25, 27 June 2006 (UTC)
WikiProject class rating edit
This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 10:04, 10 November 2007 (UTC)
What are the arrows? edit
The article currently reads, "In mathematics, a symplectomorphism is an isomorphism in the category of symplectic manifolds." The category of symplectic manifolds and what? What are the arrows? Trevorgoodchild (talk) 22:37, 6 March 2009 (UTC)
- Well, for the purposes of this article, the implication is that the symplectomorphisms are the arrows. But there has been work looking at the collection of symplectic manifolds as a category with a more general notion of morphism called "Lagrangian correspondence," and I bet there are others. Orthografer (talk) 09:02, 7 March 2009 (UTC)
- Stupid question: if the symplectomorphisms are the arrows, wouldn't that mean that all morphisms in the category are isomorphisms? —Preceding unsigned comment added by 131.215.143.10 (talk) 02:06, 12 November 2009 (UTC)
- Yes. Orthografer (talk) 03:03, 12 November 2009 (UTC)
- Stupid question: if the symplectomorphisms are the arrows, wouldn't that mean that all morphisms in the category are isomorphisms? —Preceding unsigned comment added by 131.215.143.10 (talk) 02:06, 12 November 2009 (UTC)
Citations?? edit
Why is there no citation for the section "The group of (Hamiltonian) symplectomorphisms"? This is absolutely annoying. 193.175.4.194 (talk) 11:23, 8 February 2023 (UTC)