Path Sums for Propagators in Causal Sets
arXiv:2307.08864 · doi:10.1103/PhysRevD.109.046008
Abstract
A major challenge in Causal Set research is that theories need only to match general relativity and quantum field theory in the appropriate limits. This means that there should be many different ways to calculate a scalar field propagator in a causal set that match the known limits, but may give significantly different results on the small scale. In this work, we explore under what conditions a path sum will correspond to a scalar field propagator in such a way that it matches the known value in the continuum limit. A family of solutions for the path sum is found and is verified numerically in a few specific cases.
arXiv comment9 pages, 6 figures
References in corpus (10)
- The causal set approach to quantum gravity
- Feynman Propagator for a Free Scalar Field on a Causal Set
- 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
- Nonlocal Scalar Quantum Field Theory from Causal Sets
- The moduli space of isometry classes of globally hyperbolic spacetimes
- The Discrete Geometry of a Small Causal Diamond
- A Note on analytic formulas of Feynman propagators in position space
- Light, Links and Causal Sets