Generally covariant dynamical reduction models and the Hadamard condition

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 rôle 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.

V2: 20 pages. Some typos corrected and new remarks in the Introduction. For an extended version of this paper see V1

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