An Integration Formula for the Moment Maps of Circle Actions

Details An Integration Formula for the Moment Maps of Circle Actions An Integration Formula for the Moment Maps of Circle Actions

1992-12-11

arxiv.org/abs/hep-th/9212071v2

Lett.Math.Phys. 29 (1993) 311-328

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX file, 17 pages (typos corrected, include non-isolated fixed pts)

Scientific paper

10.1007/BF00750965

The integration of the exponential of the square of the moment map of the circle action is studied by a direct stationary phase computation and by applying the Duistermaat-Heckman formula. Both methods yield two distinct formulas expressing the integral in terms of contributions from the critical set of the square of the moment map. The cohomological pairings on the symplectic quotient, including its volume (which was known to be a piecewise polynomial), are computed explicitly using the asymptotic behavior of the two formulas.

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