Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity II

TL;DR

This paper presents techniques and proofs to verify the consistency of volume and triad operator quantisation in Loop Quantum Gravity, addressing foundational issues in the quantisation process.

Contribution

It introduces new methods and rigorous proofs for the consistency of key operators in Loop Quantum Gravity, advancing the theoretical framework.

Findings

Validated the consistency of volume and triad operators

Provided rigorous mathematical proofs for operator quantisation

Strengthened the theoretical foundations of Loop Quantum Gravity

Abstract

In this paper we provide the techniques and proofs for the resuls presented in our companion paper concerning the consistency check on volume and triad operator quantisation in Loop Quantum Gravity.