Structure of the Semi Classical Scattering Matrix for General Scattering Relations

Ivana Alexandrova University of Toronto, Canada

We will show that the scattering amplitude for short range potential perturbations of the Laplacian, when restricted away from the diagonal in 𝕊^{n−1} × 𝕊^{n−1}, quantizes the natural scattering relation in the sense of semi-classical Fourier integral operators. In the case of a compactly supported perturbation the result holds near the diagonal in 𝕊^{n−1} × 𝕊^{n−1} as well. We will then show how, under a certain geometric assumption, this implies an oscillatory integral representation of the scattering amplitude the phase in which is given by the (modified) action.