Scalar Field Theory on a Causal Set in Histories Form

Abstract

We recast into histories-based form a quantum field theory defined earlier in operator language for a free scalar field on a background causal set. The resulting decoherence-functional resembles that of the continuum theory. The counterpart of the d'Alembertian operator is nonlocal and is a generalized inverse of the discrete retarded Green function. We comment on the significance of this and we also suggest how to include interactions.

plainTeX, 25 pages, no figures. One paragraph added, other small changes. Most current version is available at http://www.perimeterinstitute.ca/personal/rsorkin/some.papers/142.causet.dcf.pdf (or wherever my home-page may be, such as http://www.physics.syr.edu/~sorkin/some.papers/)

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• On a Recent Construction of "Vacuum-like" Quantum Field States in Curved Spacetime
• Quantum States as Ordinary Information
• Entanglement Entropy in Causal Set Theory
• A Ground State for the Causal Diamond in 2 Dimensions
• From Green Function to Quantum Field
• Towards Spacetime Entanglement Entropy for Interacting Theories
• Spacetime Entanglement Entropy in 1+1 Dimensions
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• A Canonical Complex Structure and the Bosonic Signature Operator for Scalar Fields in Globally Hyperbolic Spacetimes
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