\begin{definition}[Definition:Poisson Bracket]
For $n \in \N$, let:
:$\map A {x, \mathbf y, \mathbf p}: \R^{2 n + 1} \to \R$
:$\map B {x, \mathbf y, \mathbf p}: \R^{2 n + 1} \to \R$
be real functions, dependent on canonical variables.
The '''Poisson bracket''' of functions $A$ and $B$ is defined as:
:$\ds \sqbrk {A, B} := \sum_{i \mathop = 1}^n \paren {\frac {\partial A} {\partial y_i} \frac {\partial B} {\partial p_i} - \frac {\partial B} {\partial y_i} \frac {\partial A} {\partial p_i} }$
where the notation $\dfrac {\partial A} {\partial y_i}$ denotes partial differentiation.
{{NamedforDef|Siméon-Denis Poisson|cat = Poisson}}
\end{definition}