Self-Adjointness in Klein-Gordon Theory on Globally Hyperbolic Spacetimes

TL;DR

This paper proves the essential self-adjointness of the Klein-Gordon operator's spatial part on a broad class of globally hyperbolic spacetimes, advancing mathematical understanding in quantum field theory in curved spacetime.

Contribution

It introduces new functional analytic methods and results on globally hyperbolic manifolds to establish self-adjointness of the Klein-Gordon operator with external potential.

Findings

Proved essential self-adjointness for a wide class of spacetimes.

Developed new techniques combining geometry and functional analysis.

Enhanced mathematical framework for quantum field theory in curved spacetime.

Abstract

We prove essential self-adjointness of the spatial part of the linear Klein-Gordon operator with external potential for a large class of globally hyperbolic manifolds. The proof is conducted by a fusion of new results concerning globally hyperbolic manifolds, the theory of weighted Hilbert spaces and related functional analytic advances.