Type: Article

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

Much, Albert; Oeckl, Robert;

Abstract:

We show that the spatial part of the linear Klein-Gordon operator for a massive scalar field with external potential in a globally hyperbolic spacetime is a strictly positive essentially self-adjoint operator. The proof is conducted by a fusion of new results concerning globally hyperbolic manifolds, the theory of weighted Hilbert spaces and operational analytic advances in the aforementioned area.