Definition:Poisson Bracket

Definition
Let $A=\map A{x,\langle y_i\rangle_{1\mathop\le i\mathop\le n},\langle p_i\rangle_{1\mathop\le i\mathop\le n} }$ and $B=\map B {x,\langle y_i\rangle_{1\mathop\le i\mathop\le n},\langle p_i\rangle_{1\mathop\le i\mathop\le n} }$ be real functions, dependent on canonical variables.

Then:


 * $\displaystyle\sqbrk{A,B}=\sum_{i\mathop=1}^n\paren{\frac{\partial A}{\partial y_i}\frac{\partial B}{\partial p_i}-\frac{\partial B}{\partial y_i}\frac{\partial A}{\partial p_i} }$

is called the Poisson Bracket of functions $A$ and $B$.