The Sorkin-Johnston State in a Patch of the Trousers Spacetime

TL;DR

This paper investigates a quantum scalar field in a 1+1 dimensional topology-changing spacetime called the trousers spacetime, revealing that the Sorkin-Johnston state leads to divergent energy localized on both the past and future light cones of the singularity.

Contribution

It demonstrates that the Sorkin-Johnston state in a trousers spacetime results in divergent energy localized on both cones, highlighting the effects of topology change and time reversal symmetry.

Findings

Divergent energy localized on the light cones of the singularity.

Symmetry group of the patch is the dihedral group.

Topology change causes pathological energy divergence.

Abstract

A quantum scalar field in a patch of a fixed, topology-changing, $1+1$ dimensional "trousers" spacetime is studied using the Sorkin-Johnston formalism. The isometry group of the patch is the dihedral group, the symmetry group of the square. The theory is shown to be pathological in a way that can be interpreted as the topology change giving rise to a divergent energy, in agreement with previous results. In contrast to previous results, it is shown that the infinite energy is localised not only on the future light cone of the topology changing singularity, but also on the past cone, due to the time reversal symmetry of the Sorkin-Johnston state.