An Evolution Equation Approach to the Klein-Gordon Operator on Curved Spacetime

Abstract

We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of the electromagnetic potential and of the scalar potential. Our main goal is a construction of various kinds of propagators needed in quantum field theory.

44 pages

References in corpus (2)

• On the adiabatic limit of Hadamard states
• Green operators for low regularity spacetimes

Cited by in corpus (16)

• Algebraic Classical and Quantum Field Theory on Causal Sets
• Limiting absorption principle and equivalence of Feynman propagators on asymptotically Minkowski spacetimes
• 1-dimensional Schrodinger operators with complex potentials
• Self-Adjointness in Klein-Gordon Theory on Globally Hyperbolic Spacetimes
• A remark on the essential self-adjointness for Klein-Gordon type operators
• Essential self-adjointness for the Klein-Gordon type operators on asymptotically static spacetime
• The Cosmological Semiclassical Einstein Equation as an Infinite-Dimensional Dynamical System
• Analytic semigroups approaching a Schrödinger group on real foliated metric manifolds
• Spatially flat FLRW spacetimes with a Big Bang from matrix geometry
• On Global Hyperbolicity of Spacetimes: Topology Meets Functional Analysis
• Bogolyubov invariant via relative spectral invariants on manifolds
• A Canonical Complex Structure and the Bosonic Signature Operator for Scalar Fields in Globally Hyperbolic Spacetimes
• Adiabatic Ground States in Non-Smooth Spacetimes
• Gravitational Waves beyond the Linear Approximation and Gravitational Wave Reflection
• Global Hyperbolicity and Self-adjointness
• Remarks on the geodesically completeness and the smoothing effect on asymptotically Minkowski spacetimes