Poisson bracket

tendor

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.