Let a compact Lie group $G$ acts on a closed symplectic manifold $(M,\omega)$. If the action is Hamiltonian with $\mu$ the moment map, then the integral $$\int\_M e^{i\mu (X)+\omega}$$ is equal to the first term in the stationary phase approximation.


My question is if there is a similar integral formula for a compact $M$ with boundary.



Duistermaat-Heckman integral formula on compact manifold with boundary
There is the paper by [E. Prato and and S. Wu](http://arxiv.org/pdf/alg-geom/9307005.pdf), 1993 which deals with (at least) a special case of this.


