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

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.

12 pages; v2: generalized main result, added section on geodesic completeness, minor corrections, added references; v3: improved structure of Sections 4 and 5, minor corrections, added references; v4: final corrections

References in corpus (4)

• Quantum Gowdy $T^3$ Model: Schrodinger Representation with Unitary Dynamics
• An Evolution Equation Approach to the Klein-Gordon Operator on Curved Spacetime
• A Note on Non-compact Cauchy surface
• On sliced spaces: Global Hyperbolicity revisited

Cited by in corpus (9)

• Boson stars and their relatives in semiclassical gravity
• Observables in Quantum Mechanics and the Importance of Self-adjointness
• Complex Structures for Klein-Gordon Theory on Globally Hyperbolic Spacetimes
• Quantum evolution of the Hawking state for black holes
• Perturbative quantum evolution of the gravitational state and dressing in general backgrounds
• Strict deformations of quantum field theory in de Sitter spacetime
• On Global Hyperbolicity of Spacetimes: Topology Meets Functional Analysis
• A Canonical Complex Structure and the Bosonic Signature Operator for Scalar Fields in Globally Hyperbolic Spacetimes
• Global Hyperbolicity and Self-adjointness