Construction of Hadamard states by pseudo-differential calculus

TL;DR

This paper introduces a novel pseudo-differential calculus method to construct Hadamard states for Klein-Gordon equations on certain space-times, enabling the creation of all pure states and analyzing their symplectic covariance.

Contribution

It presents a new pseudo-differential calculus approach to construct Hadamard states, including pure states, on a broad class of space-times, extending previous methods.

Findings

Constructed all pure Hadamard states using pseudo-differential calculus.

Analyzed covariance properties of Hadamard states under symplectic transformations.

Extended the construction to arbitrary globally hyperbolic space-times.

Abstract

We give a new construction based on pseudo-differential calculus of quasi-free Hadamard states for Klein-Gordon equations on a class of space-times whose metric is well-behaved at spatial infinity. In particular we construct all pure Hadamard states and study their covariance under symplectic transformations. Using our results we give a new construction of Hadamard states on arbitrary globally hyperbolic space-times.