In mathematics, the Duistermaat–Heckman formula, due to , states that the
pushforward of the canonical (
Liouville) measure on a
symplectic manifold
In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, M , equipped with a closed nondegenerate differential 2-form \omega , called the symplectic form. The study of symplectic manifolds is called sy ...
under the
moment map is a piecewise polynomial measure. Equivalently, the
Fourier transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...
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
In mathematics, particularly in integral calculus, the localization theorem allows, under certain conditions, to infer the nullity of a function (mathematics), function given only information about its continuity (mathematics), continuity and the v ...
for
equivariant cohomology.
References
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External links
*http://terrytao.wordpress.com/2013/02/08/the-harish-chandra-itzykson-zuber-integral-formula/
{{DEFAULTSORT:Duistermaat-Heckman formula
Symplectic geometry