Quantum Gravity and Regge Calculus

TL;DR

This paper reviews canonical general relativity and its quantum implications, comparing continuum and Regge calculus discretizations, and critiques the derivation of quantum discrete space structures.

Contribution

It provides an informal comparison of different formulations of quantum gravity and highlights potential flaws in deriving discrete quantum space from Regge calculus.

Findings

Discussions on canonical general relativity formulations

Comparison between continuum and discretized approaches

Identification of a flaw in deriving quantum discrete space

Abstract

This is an informal review of the formulation of canonical general relativity and of its implications for quantum gravity; the various versions are compared, both in the continuum and in a discretized approximation suggested by Regge calculus. I also show that the weakness of the link with the geometric content of the theory gives rise to what I think is a serious flaw in the claimed derivation of a discrete structure for space at the quantum level.