Let M be a symplectic manifold, that is, a manifold equipped with a symplectic form : a 2-form ω ω which is both closed (i.e., its exterior derivative d ω ω vanishes) and non-degenerate. For example, in the treatment above, take M to be R 2 n and take ω ω = ∑ ∑ i = 1 n d q i ∧ ∧ d p i .