Talk:Poisson bracket

message: Regarding the statement that "the smooth functions on a symplectic manifold are naturally a Poisson algebra" (paraphrase):
I changed the link from Symplectic space to Symplectic manifold since manifolds are the objects with smooth functions, and 'symplectic space' refers (at least in WP) to either symplectic vector space or symplectic manifold.  The natural domain of the "smooth functions on" functor is the category of manifolds, so it seems to be unambiguous. Sympleko 19:07, 19 Apr 2005 (UTC)
thread_title:  Disambiguation 

message: Why is there a link to "superPoisson algebra"-s but not to "Poisson algebra"-s? I don't quite understand how the former are closer related.
:Poisson algebra is linked from the second sentence at the top of the article, so does not need a "see also" link.  -lethe talk [ +] 04:26, 11 July 2006 (UTC)
thread_title:  a link to poisson algebras in the "see also" section 

message: The general definition given here, while correct, seems to be overly verbose. I believe that one can much more simply define the Poisson bracket by noting that if the symplectic form is nondegenerate, then it has an inverse tensor w-1. Then one defines {f,g}:=w-1(df, dg) (see for example the PlanetMath site, which has this much simpler description). This is much simpler than the lengthy definition given, although the details discussed there are perhaps sufficiently important to warrant keeping them. However, perhaps we should put this shorter version in as well? Mad2Physicist (talk) 08:05, 25 November 2008 (UTC)
thread_title:  General definition 

message: Much of the intro paragraph here was covered in the previous section.  The statement that the Lie algebra of functions under the PB is the Lie algebra of the group of symplectomorphisms is, I believe, incorrect--it is the Lie algebra of symplectic vector fields which is.  This is the same as functions MODULO locally constant functions...  As a result, I changed the title.  Finally, I changed "vector field on the tangent bundle" to "vector field on the configuration space."
Frankly, I wasn't sure about the importance of this result and whether it merited inclusion in the article, but I didn't want to just remove the section.  But as far as I'm concerned, it could be deleted.  Natkuhn (talk) 05:09, 24 December 2012 (UTC)
thread_title: Lie algebra

message: May i suggest that the current introduction is unintelligible to most people? Could someone rephrase it to introduce the basic concept in less technical terms?Richwil (talk) 18:30, 21 January 2009 (UTC)
thread_title: Introduction

message: If nobody objects then I shall remove the animated graphics. The graphics only illustrates trivial and unrelated matter at an inappropriate level. It doesn't explain anything. The animation only catches the eye and makes it difficult to read the text.  —Preceding unsigned comment added by Rdengler (talk • contribs) 07:23, 16 May 2009 (UTC)
thread_title: Animated Graphics

message: There is field theoretical Poisson bracket expressed as an integral instead of a sum, and the partial derivatives become functional derivatives. It deserves at least a section in this article, or perhaps its own article. It would be nice if somebody feels a sudden urge to write it. A reference could be Walter Greiner, "Field Quantization". YohanN7 (talk) 21:35, 7 April 2013 (UTC)
thread_title:  Field Theoretical Poisson Bracket 

message: Another article written by some expert who can't relate his knowledge to the world of non-experts. Wikipedia is getting worse every day!  — Preceding unsigned comment added by Koitus~nlwiki (talk • contribs) 13:41, 3 August 2020 (UTC)
replies: text: This material is inherently more advanced. Recommended material to learn first is Hamiltonian systems, some examples, Lie derivative, Liouville's theorem, symplectic form.
194.230.148.166 (talk) 21:11, 24 October 2022 (UTC)
thread_title:  Explain, please! 

message: "Furthermore, according to Poisson's Theorem, if two quantities  and  are explicitly time independent () constants of motion, so is their Poisson bracket . This does not always supply a useful result, however, since the number of possible constants of motion is limited ( for a system with degrees of freedom), and so the result may be trivial (a constant, or a function of A and B.)"
But isn't this method quite productive in infinite dimensions?
194.230.148.166 (talk) 21:08, 24 October 2022 (UTC)
thread_title:  Generating new invariants via the Poisson bracket 

message: The Poisson bracket also distinguishes a certain class of coordinate transformations, called canonical transformations, which map canonical coordinate systems into canonical coordinate systems 173.68.173.92 (talk) 04:37, 10 August 2023 (UTC)
thread_title:  Is this a mistake in the post?