Poisson bracket


by tendor
Tags: bracket, poisson
tendor
tendor is offline
#1
Dec8-10, 03:53 AM
P: 11
Hi,
I have a small problem about PB. I think I know the answer, but I want to make sure it's correct.

For example lets have cartesian n dimensional problem with N particles, then PB becomes
[tex]
\left\{F(\vec x^1,\cdots,\vec x^N,\vec p^1,\cdots,\vec p^N),G(\vec x^1,\cdots,\vec x^N,\vec p^1,\cdots,\vec p^N)\right\} =\sum\limits_{a=1}^{N}\sum\limits_{i=1}^{n}\frac{\partial F}{\partial x^a_i}\frac{\partial G}{\partial p^a_i}-\frac{\partial F}{\partial p^a_i}\frac{\partial G}{\partial x^a_i}
[/tex]

Is there somebody who could confirm me my supposition or send me some link about this (because I haven't found anything, just one particle situations which are not very helpful).

Thanks T.
Phys.Org News Partner Science news on Phys.org
Better thermal-imaging lens from waste sulfur
Hackathon team's GoogolPlex gives Siri extra powers
Bright points in Sun's atmosphere mark patterns deep in its interior

Register to reply

Related Discussions
Poisson bracket Quantum Physics 14
poisson bracket Classical Physics 0
Poisson bracket and Lax pairs General Math 0
Poisson Bracket Introductory Physics Homework 1
about the basics of Poisson bracket Differential Geometry 3