In canonical coordinates (also known as Darboux coordinates) ( q i , p i ) on the phase space, given two functions f ( p i , q i , t ) and g ( p i , q i , t ) , the Poisson bracket takes the form { f , g } = ∑ ∑ i = 1 N ( ∂ ∂ f ∂ ∂ q i ∂ ∂ g ∂ ∂ p i − − ∂ ∂ f ∂ ∂ p i ∂ ∂ g ∂ ∂ q i ) .