Lightcone constraint in 3D simplicial gravity: method and application to quantum time order

Description

Title: Quantum gravity and time order

Abstract: In Lorentzian simplicial gravity, a lightcone constraint needs to be imposed to ensure regular lightcone structure. The lack of a systematic method to impose the lightcone constraint in higher than 2 dimensions presents an obstacle in proving ergodicity for Monte Carlo simulation algorithm of locally causal dynamical triangulation, in applying Monte Carlo simulation for Lorentzian simplicial quantum gravity, and in studying superposition of time order. In this work, we provide a method to compute the lightcone numbers at any point of a 3D Lorentzian simplicial geometry, which allows the imposition of the lightcone constraint. The method is applied to show that simplicial geometries realizing superposition of time order is generically present in 3D. The method should also be useful in Monte Carlo simulations for Lorentzian quantum gravity, and in further extensions of the method to higher dimensions. A Mathematica notebook is provided with the source code of the method for applications.

This product contains an article in .pdf format and an accompanying Mathematica notebook in .nb format. The purchase includes all future versions of the article and the notebook.

Version history

• Original versions: Article v1.0; Notebook v1.0
• Updated edge lightcone numbers: Article v1.1; Notebook v1.1