Degrees of freedom in discrete geometry

TL;DR

This paper explores the geometric variables of simplices in discrete geometry, introducing new formulations and methods to analyze degrees of freedom in discrete gravity systems.

Contribution

It presents novel vectorial and coordinate-free descriptions of simplices and a systematic approach to couple particles of space and compute degrees of freedom.

Findings

New vectorial and coordinate-free formulations of simplices

A consistent method to couple particles of space

Calculation of degrees of freedom in classical discrete space systems

Abstract

Following recent developments in discrete gravity, we study geometrical variables (angles and forms) of simplices in the discrete geometry point of view. Some of our relatively new results include: new ways of writing a set of simplices using vectorial (differential form) and coordinate-free pictures, and a consistent procedure to couple particles of space, together with a method to calculate the degrees of freedom of the system of 'quanta' of space in the classical framework.