Generally covariant dynamical reduction models and the Hadamard condition

TL;DR

This paper extends dynamical reduction models to curved spacetimes, ensuring they preserve the Hadamard condition, and explores their potential role in semiclassical gravity with explicit energy-momentum violation estimates.

Contribution

It introduces a class of generally covariant relativistic collapse models that maintain the Hadamard condition and analyzes their implications for semiclassical gravity.

Findings

Collapse operators map initial Hadamard states to final Hadamard states

Explicit calculation of energy-momentum violations due to state reduction

Proposed models may play a role in semiclassical gravity theories

Abstract

We provide general guidelines for generalizing dynamical reduction models to curved spacetimes and propose a class of generally covariant relativistic versions of the GRW model. We anticipate that the collapse operators of our class of models may play a r\^ole in a yet-to-be-formulated theory of semiclassical gravity with collapses. We show explicitly that the collapse operators map a dense domain of states that are initially Hadamard to final Hadamard states -- a property that we expect will be needed for the construction of such a semiclassical theory. Finally, we provide a simple example in which we explicitly compute the violations in energy-momentum due to the state reduction process and conclude that this violation is of the order of a parameter of the model -- supposed to be small.