Poisson Bracket

Let $F$ and $G$ be infinitely differentiable functions of $x$ and $p$. Then the Poisson bracket is defined by

$$(F,G)=\sum_{\nu=1}^n \left({{\partial F\over\partial p_\nu}{... ... G\over\partial p_\nu}{\partial F\over\partial x_\nu}}\right).$$

If $F$ and $G$ are functions of $x$ and $p$ only, then the Lagrange Bracket $[F,G]$ collapses the Poisson bracket $(F,G)$.

See also Lagrange Bracket, Lie Bracket

References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1004, 1980.