Adiabatic Vacua and Hadamard States for Scalar Quantum Fields on Curved Spacetime

TL;DR

This paper develops a criterion for identifying Hadamard states of scalar quantum fields on curved spacetimes, demonstrating that certain known states are Hadamard and addressing the general construction problem.

Contribution

It introduces a pseudodifferential operator and wavefront set-based criterion for Hadamard states, advancing the understanding of quantum field states on curved spacetime.

Findings

Ground- and KMS-states on static spacetimes are Hadamard.

Adiabatic vacuum states on Robertson-Walker spaces are Hadamard.

The construction of Hadamard states on arbitrary curved spacetimes is addressed.

Abstract

Quasifree states of a linear Klein-Gordon quantum field on globally hyperbolic spacetime manifolds are considered. Using techniques from the theory of pseudodifferential operators and wavefront sets on manifolds a criterion for a state to be an Hadamard state is developed. It is shown that ground- and KMS-states on certain static spacetimes and adiabatic vacuum states on Robertson-Walker spaces are Hadamard states. Finally, the problem of constructing Hadamard states on arbitrary curved spacetimes is solved in principle.