Numerical Evaluation of the Causal Set Propagator in 2D Anti-de Sitter Spacetime

Abstract

We numerically investigate the application of the path-sum-based causal set scalar propagator construction to (1+1)-dimensional Anti-de Sitter (AdS) spacetime. Building upon a generalization of Johnston's path sum approach, we simulate Poisson-sprinkled causal sets in AdS${}_{1+1}$ and numerically evaluate the retarded scalar propagator, comparing it to the known continuum result. Our results confirm that even in curved spacetimes with constant negative curvature, the discrete causal set path sum reproduces the continuum propagator without modification of the flat-spacetime jump amplitudes, thereby providing further numerical support for former analytical results and the applicability of the path sum formalism to curved Lorentzian manifolds.

arXiv comment15 pages, 8 figures

References in corpus (28)

• Quantum Gravity: a Progress Report
• A Classical Sequential Growth Dynamics for Causal Sets
• The causal set approach to quantum gravity
• Gravity and the Crossed Product
• Quantum Gravity Phenomenology, Lorentz Invariance and Discreteness
• The Scalar Curvature of a Causal Set
• The Universe from Scratch
• Causal set d'Alembertians for various dimensions
• Particle propagators on discrete spacetime
• Sum-over-histories origin of the composition laws of relativistic quantum mechanics and quantum cosmology
• Generalized Causal Set d'Alembertians
• Towards a Definition of Locality in a Manifoldlike Causal Set
• Nonlocal Scalar Quantum Field Theory from Causal Sets
• A closed form expression for the causal set d'Alembertian
• Quantum reference frames, measurement schemes and the type of local algebras in quantum field theory
• Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings
• The Discrete Geometry of a Small Causal Diamond
• Studies on the SJ Vacuum in de Sitter Spacetime
• Algebraic Classical and Quantum Field Theory on Causal Sets
• The Random Discrete Action for 2-Dimensional Spacetime
• Scalar Field Green Functions on Causal Sets
• The Sorkin-Johnston State in a Patch of the Trousers Spacetime
• Sorkin-Johnston vacuum for a massive scalar field in the 2D causal diamond
• Path Sums for Propagators in Causal Sets
• Universal behaviour of generalized Causal set d'Alembertians in curved spacetime
• Local Structure of Sprinkled Causal Sets
• A Tale of Two Actions: A Variational Principle for Two-Dimensional Causal Sets
• Asymptotic error in the eigenfunction expansion for the Green's function of a Sturm-Liouville problem