Poissonklammer

$\{f,g\}=\sum _k(\frac{\partial f}{\partial q_k}\frac{\partial g}{\partial p_k}-\frac{\partial f}{\partial p_k}\frac{\partial g}{\partial q_k})$

invarianz

${\{f,g\}}_{q,p}={\{f,g\}}_{Q,P}=\{f,g\}$

fundamentale

$\{q_k,p_l\}={\delta }_{kl}$

$\{q_k,q_l\}=\{p_k,p_l\}=0$