Abstract

Abstract:

We consider the massive Klein-Gordon equation on asymptotically Minkowski spacetimes, in the sense that the manifold is $\Bbb{R}^{1+d}$ and the metric approaches that of Minkowski space at infinity in a short-range way, jointly in time and space variables. In this setup we define Feynman and anti-Feynman scattering data and prove the Fredholm property of the Klein-Gordon operator with the associated generalized Atiyah-Patodi-Singer type boundary conditions at infinite times. We then construct a parametrix (with compact remainder terms) for the Fredholm problem and prove that it is also a Feynman parametrix in the sense of Duistermaat and H\"ormander.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1501-1546
Launched on MUSE
2019-11-02
Open Access
No
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