On a Recent Construction of "Vacuum-like" Quantum Field States in Curved Spacetime

Abstract

Afshordi, Aslanbeigi and Sorkin have recently proposed a construction of a distinguished "S-J state" for scalar field theory in (bounded regions of) general curved spacetimes. We establish rigorously that the proposal is well-defined on globally hyperbolic spacetimes or spacetime regions that can be embedded as relatively compact subsets of other globally hyperbolic spacetimes, and also show that, whenever the proposal is well-defined, it yields a pure quasifree state. However, by explicitly considering portions of ultrastatic spacetimes, we show that the S-J state is not in general a Hadamard state. In the specific case where the Cauchy surface is a round 3-sphere, we prove that the representation induced by the S-J state is generally not unitarily equivalent to that of a Hadamard state, and indeed that the representations induced by S-J states on nested regions of the ultrastatic spacetime also fail to be unitarily equivalent in general. The implications of these results are discussed.

25pp, LaTeX. v2 References added, typos corrected. To appear in Class Quantum Gravity

References in corpus (3)

• Feynman Propagator for a Free Scalar Field on a Causal Set
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• Quantum Field Theory in Curved Spacetime (2nd Edition)
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• Spacetime Entanglement Entropy: Covariance and Discreteness
• Coupling the Sorkin-Johnston State to Gravity
• Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes
• A Canonical Complex Structure and the Bosonic Signature Operator for Scalar Fields in Globally Hyperbolic Spacetimes
• Quantization, dequantization, and distinguished states
• On the (Non)Hadamard Property of the SJ State in a $1+1$D Causal Diamond
• Aspects of Quantum Fields on Causal Sets