"Vacuum-like" Hadamard states for quantum fields on curved spacetimes

TL;DR

This paper introduces a modified Sorkin-Johnston state for scalar quantum fields on certain curved spacetimes, ensuring Hadamard property through a smooth cutoff, but losing uniqueness due to smoothing.

Contribution

It proposes a smoothing modification to the Sorkin-Johnston states that guarantees Hadamard states on globally hyperbolic spacetimes with compact Cauchy surfaces.

Findings

Modified states are always Hadamard.

Smoothing removes the uniqueness of the original states.

The approach applies to a class of globally hyperbolic spacetimes.

Abstract

We present a modification of the recently proposed Sorkin-Johnston states for scalar free quantum fields on a class of globally hyperbolic spacetimes possessing compact Cauchy hypersurfaces. The modification relies on a smooth cutoff of the commutator function and leads always to Hadamard states, in contrast to the original Sorkin-Johnston states. The modified Sorkin-Johnston states are, however, due to the smoothing no longer uniquely associated to the spacetime.