2018/05/28 by Roman Sverdlov, Sverdlov, Roman
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #gr-qc
paper · pdf · doi:10.48550/arxiv.1805.11420
11 pages, no figures
openalex publication_date 2018/05/28 · openalex created_date 2018/06/13 · arxiv created 2018/06/26 · arxiv updated 2018/06/27 · openalex updated_date 2026/07/28
In this paper we address the non-locality issue of quantum field theory on a causal set by rewriting it in such a way that avoids the use of d'Alembertian. We do that by replacing scalar field over points with scalar field over edges, where the edges are taken to be very long rather than very short. In particular, they are much longer than the size of the laboratory. Due to their large length, we can single out the edges that are almost parallel to each other, and then use directional derivatives in the direction of those edges (as opposed to d'Alembertian) along with a constraint that the derivatives are small in the direction perpendicular to those edges, in order to come up with a plane wave. The scalar field is thought to reside at the future end of those edges, which renders the seemingly nonlocal effects of their large length as physically irrelevant. After that we add by hand the interaction of those plane waves that would amount to 4-vertex coupling of plane waves.