Adiabatic Ground States in Non-Smooth Spacetimes

TL;DR

This paper demonstrates that in non-smooth ultrastatic spacetimes, the Klein-Gordon ground state is an adiabatic state whose order correlates with the metric's regularity, using microlocal and spectral analysis techniques.

Contribution

It establishes a link between the regularity of spacetime metrics and the nature of ground states in quantum field theory, extending understanding to non-smooth geometries.

Findings

Ground state is an adiabatic state in non-smooth spacetimes

Order of the adiabatic state depends linearly on metric regularity

Uses microlocal estimates and eigenvalue asymptotics for analysis

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.