A note on area variables in Regge calculus

TL;DR

This paper explores a novel approach to Regge calculus in four dimensions by using triangle areas instead of edge lengths as fundamental variables, discussing associated challenges and limitations.

Contribution

It introduces the concept of area-based variables in Regge calculus and analyzes the potential difficulties of this approach.

Findings

Identifies key restrictions of area variables in Regge calculus

Highlights challenges in formulating a consistent area-based model

Discusses implications for discrete gravity theories

Abstract

We consider the possibility of setting up a new version of Regge calculus in four dimensions with areas of triangles as the basic variables rather than the edge-lengths. The difficulties and restrictions of this approach are discussed.