{ f , g } = ∑ k ( ∂ f ∂ q k ∂ g ∂ p k − ∂ f ∂ p k ∂ g ∂ q k ) {\displaystyle \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)}}
{ f , g } q , p = { f , g } Q , P = { f , g } {\displaystyle {{\left\{f,g\right\}}_{q,p}}={{\left\{f,g\right\}}_{Q,P}}=\left\{f,g\right\}}
{ q k , p l } = δ k l {\displaystyle \left\{{{q}_{k}},{{p}_{l}}\right\}={{\delta }_{kl}}}
{ q k , q l } = { p k , p l } = 0 {\displaystyle \left\{{{q}_{k}},{{q}_{l}}\right\}=\left\{{{p}_{k}},{{p}_{l}}\right\}=0}
