Constraints on Area Variables in Regge Calculus

TL;DR

This paper presents a general method for deriving constraints between area variables in area Regge calculus, demonstrated on a simple 4-sphere tessellation, linking constraints to Regge equations of motion.

Contribution

It introduces a new systematic approach to identify independent area constraints in Regge calculus, connecting them directly to equations of motion.

Findings

Number of independent constraints equals the difference between triangles and edges.

Constraints derived imply the Regge equations of motion.

Method applicable to simple tessellations of the 4-sphere.

Abstract

We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4-sphere. The number of independent constraints on the variations of the triangle areas is shown to equal the difference between the numbers of triangles and edges, and a general method of choosing independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example.