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.
References
External links http://terrytao.wordpress.com/2013/02/08/the-harish-chandra-itzykson-zuber-integral-formula/