Duistermaat–Heckman formula

In mathematics, the Duistermaat–Heckman formula, due to Duistermaat and Heckman (1982), 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.

(Berline Vergne) and, independently, (Atiyah Bott) showed how to deduce the Duistermaat–Heckman formula from a localization theorem for equivariant cohomology.

References

• Berline, Nicole; Vergne, Michele (1982), "Classes caracteristiques equivariantes. Formule de localisation en cohomologie equivariante", Comptes rendus de l'Académie des sciences 
• Atiyah, Michael Francis; Bott, Raoul (1984), "The moment map and equivariant cohomology", Topology 23 (1): 1–28, doi:10.1016/0040-9383(84)90021-1 
• Duistermaat, J. J.; Heckman, G. J. (1982), "On the variation in the cohomology of the symplectic form of the reduced phase space", Inventiones Mathematicae 69 (2): 259–268, doi:10.1007/BF01399506 

External links

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