In mathematics, the Duistermaat–Heckman formula, due to, states that the pushforward of the canonical (Liouville) measure on a symplectic manifold under the moment map is a piecewise polynomial measure. Equivalently, the Fourier transform of the canonical measure is given exactly by the stationary phase approximation.
and, independently, showed how to deduce the Duistermaat–Heckman formula from a localization theorem for equivariant cohomology.