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

Accepted for publication in CQG. Added Theorem 3.0.1 proving the purity of the states, added Theorem A.1 proving the essential self-adjointness of the elliptic operator. References were also added