Feynman propagators and Hadamard states from scattering data for the Klein-Gordon equation on asymptotically Minkowski spacetimes
arXiv:1603.07465
Abstract
We consider the massive Klein-Gordon equation on a class of asymptotically static spacetimes. We prove the existence and Hadamard property of the in and out states constructed by scattering theory methods. Assuming in addition that the metric approaches that of Minkowski space at infinity in a short-range way, jointly in time and space variables, we define Feynman scattering data and prove the Fredholm property of the Klein-Gordon operator with the associated Atiyah-Patodi-Singer boundary conditions. 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{ö}rmander.
References in corpus (12)
- Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction
- A scattering theory for the wave equation on Kerr black hole exteriors
- The Hadamard Condition for Dirac Fields and Adiabatic States on Robertson-Walker Spacetimes
- A smooth introduction to the wavefront set
- Uniqueness theorem for BMS-invariant states of scalar QFT on the null boundary of asymptotically flat spacetimes and bulk-boundary observable algebra correspondence
- Hadamard states for the Klein-Gordon equation on Lorentzian manifolds of bounded geometry
- An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
- Construction of Hadamard states by characteristic Cauchy problem
- Adiabatic Vacua and Hadamard States for Scalar Quantum Fields on Curved Spacetime
- Asymptotics of radiation fields in asymptotically Minkowski space
- Asymptotic completeness for superradiant Klein-Gordon equations and applications to the De Sitter Kerr metric
- On t-dependent hyperbolic systems. Part 2