Scalar Field Green Functions on Causal Sets

Abstract

We examine the validity and scope of Johnston's models for scalar field retarded Green functions on causal sets in 2 and 4 dimensions. As in the continuum, the massive Green function can be obtained from the massless one, and hence the key task in causal set theory is to first identify the massless Green function. We propose that the 2-d model provides a Green function for the massive scalar field on causal sets approximated by any topologically trivial 2 dimensional spacetime. We explicitly demonstrate that this is indeed the case in a Riemann normal neighbourhood. In 4-d the model can again be used to provide a Green function for the massive scalar field in a Riemann normal neighbourhood which we compare to Bunch and Parker's continuum Green function. We find that the same prescription can also be used for deSitter spacetime and the conformally flat patch of anti deSitter spacetime. Our analysis then allows us to suggest a generalisation of Johnston's model for the Green function for a causal set approximated by 3 dimensional flat spacetime.

23 pages, 5 figures

References in corpus (5)

• Feynman Propagator for a Free Scalar Field on a Causal Set
• Particle propagators on discrete spacetime
• Generalized Causal Set d'Alembertians
• The Discrete Geometry of a Small Causal Diamond
• Correction terms for propagators and d'Alembertians due to spacetime discreteness

Cited by in corpus (10)

• The causal set approach to quantum gravity
• Studies on the SJ Vacuum in de Sitter Spacetime
• Algebraic Classical and Quantum Field Theory on Causal Sets
• Entanglement Entropy of Causal Set de Sitter Horizons
• Path length distribution in two-dimensional causal sets
• Observables for cyclic causal set cosmologies
• In-in correlators and scattering amplitudes on a causal set
• Spacetime Entanglement Entropy: Covariance and Discreteness
• Entanglement Entropy and Causal Set Theory
• Numerical Evaluation of the Causal Set Propagator in 2D Anti-de Sitter Spacetime