Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis

TL;DR

This paper analyzes the semiclassical limit of the algebraic Master constraint in Algebraic Quantum Gravity, showing it reproduces General Relativity's generators, thus supporting the inclusion of GR in AQG's semiclassical sector.

Contribution

It demonstrates that the semiclassical limit of the AQG Master constraint reproduces the correct GR generators, advancing understanding of AQG's relation to classical gravity.

Findings

Semiclassical limit reproduces GR generators

Substitution of SU(2) by U(1)^3 justified

Supports inclusion of GR in AQG semiclassical sector

Abstract

In the previous article a new combinatorial and thus purely algebraical approach to quantum gravity, called Algebraic Quantum Gravity (AQG), was introduced. In the framework of AQG existing semiclassical tools can be applied to operators that encode the dynamics of AQG such as the Master constraint operator. In this article we will analyse the semiclassical limit of the (extended) algebraic Master constraint operator and show that it reproduces the correct infinitesimal generators of General Relativity. Therefore the question whether General Relativity is included in the semiclassical sector of the theory, which is still an open problem in LQG, can be significantly improved in the framework of AQG. For the calculations we will substitute SU(2) by U(1)^3. That this substitution is justified will be demonstrated in the third article of this series