Poissonklammer

$\left\{f,g\right\}=\sum \limits _{k}{\left({\frac {\partial f}{\partial {{q}_{k}}}}{\frac {\partial g}{\partial {{p}_{k}}}}-{\frac {\partial f}{\partial {{p}_{k}}}}{\frac {\partial g}{\partial {{q}_{k}}}}\right)}$

invarianz

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

fundamentale

$\left\{{{q}_{k}},{{p}_{l}}\right\}={{\delta }_{kl}}$

$\left\{{{q}_{k}},{{q}_{l}}\right\}=\left\{{{p}_{k}},{{p}_{l}}\right\}=0$