Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis

Details Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis

2006-07-23

arxiv.org/abs/gr-qc/0607100v1

Class.Quant.Grav.24:2499-2564,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1088/0264-9381/24/10/004

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

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