Formula_1285

\[\begin{gathered}\left\{P_{i}, Q_{j}\right\} \equiv \sum_{k}\left(\frac{\partial P_{i}}{\partial p_{k}} \frac{\partial Q_{j}}{\partial q_{k}}-\frac{\partial P_{i}}{\partial q_{k}} \frac{\partial Q_{j}}{\partial p_{k}}\right)=\left\{p_{i}, q_{j}\right\}=\delta_{i j}, \\\left\{P_{i}, P_{j}\right\}=\left\{Q_{i}, Q_{j}\right\}=0,\end{gathered}\]