Measure in the 2D Regge quantum gravity

TL;DR

This paper introduces a simplified 2D Regge calculus model with equal triangle areas, making numerical simulations more straightforward compared to traditional nonlocal measures.

Contribution

It proposes a new discretization of 2D Regge calculus with equal triangle areas, simplifying the Lund-Regge measure for easier numerical analysis.

Findings

Simplified measure facilitates numerical simulations.

Model maintains key features of 2D quantum gravity.

Potential for more efficient computational studies.

Abstract

We propose a version of the 2D Regge calculus, in which the areas of all triangles are equal to each other. In this discretization Lund - Regge measure over link lengths is simplified considerably. Contrary to the usual Regge models with Lund - Regge measure, where this measure is nonlocal and rather complicated, the models based on our approach can be investigated using the numerical simulations in a rather simple way.