Adiabatic Ground States in Non-Smooth Spacetimes

Abstract

Ground states are a well-known class of Hadamard states in smooth spacetimes. In this paper we show that the ground state of the Klein-Gordon field in a non-smooth ultrastatic spacetime is an adiabatic state. The order of the state depends linearly on the regularity of the metric. We obtain the result by combining microlocal estimates for the causal propagator, propagation of singularities results for non-smooth pseudodifferential operators, and eigenvalue asymptotics for elliptic operators of low regularity.

arXiv commentarXiv admin note: text overlap with arXiv:2203.04362

References in corpus (12)

• Adiabatic vacuum states on general spacetime manifolds: Definition, construction, and physical properties
• Causality theory for closed cone structures with applications
• Non-radial oscillation modes as a probe of density discontinuities in neutron stars
• On Lorentzian causality with continuous metrics
• Passivity and microlocal spectrum condition
• The Necessity of the Hadamard Condition
• Simple Analytic Models of Gravitational Collapse
• Construction of Hadamard states by pseudo-differential calculus
• Global hyperbolicity for spacetimes with continuous metrics
• Feynman Propagators on Static Spacetimes
• An Evolution Equation Approach to the Klein-Gordon Operator on Curved Spacetime
• Green Operators in Low Regularity Spacetimes and Quantum Field Theory