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)[reply]

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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)[reply]

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)[reply]

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)[reply]

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)[reply]

Yes. Orthografer (talk) 03:03, 12 November 2009 (UTC)[reply]

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)[reply]