Quantum fields from global propagators on asymptotically Minkowski and extended de Sitter spacetimes

TL;DR

This paper develops a framework connecting propagators, symplectic forms, and quantum fields on asymptotically Minkowski and de Sitter spacetimes, enabling the construction of distinguished two-point functions and extending QFT beyond conformal boundaries.

Contribution

It introduces a method to derive quantum field theory structures from global propagators on asymptotically Minkowski and de Sitter spacetimes, linking solutions and asymptotic data.

Findings

Constructed symplectic forms from propagators on asymptotic spacetimes

Established isomorphisms between solution spaces and asymptotic data spaces

Derived distinguished Hadamard two-point functions from asymptotic data

Abstract

We consider the wave equation on asymptotically Minkowski spacetimes and the Klein-Gordon equation on even asymptotically de Sitter spaces. In both cases we show that the extreme difference of propagators (i.e. retarded propagator minus advanced, or Feynman minus anti-Feynman), defined as Fredholm inverses, induces a symplectic form on the space of solutions with wave front set confined to the radial sets. Furthermore, we construct isomorphisms between the solution spaces and symplectic spaces of asymptotic data. As an application of this result we obtain distinguished Hadamard two-point functions from asymptotic data. Ultimately, we prove that the corresponding Quantum Field Theory on asymptotically de Sitter spacetimes induces canonically a QFT beyond the future and past conformal boundary, i.e. on two even asymptotically hyperbolic spaces. Specifically, we show this to be true both at the level of symplectic spaces of solutions and at the level of Hadamard two-point functions.