Algebraic quantum gravity (AQG): II. Semiclassical analysis
Abstract
In the previous paper (Giesel and Thiemann 2006 Conceptual setup Preprint grqc/0607099) 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 paper, 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 of 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) with U(1)^{3}. That this substitution is justified will be demonstrated in the third paper (Giesel and Thiemann 2006 Semiclassical perturbation theory Preprint grqc/0607101) of this series.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 May 2007
 DOI:
 10.1088/02649381/24/10/004
 arXiv:
 arXiv:grqc/0607100
 Bibcode:
 2007CQGra..24.2499G
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 Class.Quant.Grav.24:24992564,2007