Algebraic quantum gravity

In this talk a new top down approach to canonical quantum gravity, called Algebraic Quantum Gravity (AQG) is introduced. The quantum kinematics of AQG is determined by an abstract *-algebra generated by a countable set of elementary operators labelled by an algebraic graph. The quantum dynamics of AQG is governed by a single Master Constraint operator. While AQG is inspired by Loop Quantum Gravity (LQG), it differs drastically from it because in AQG there is fundamentally no topology or differential structure. The missing information about the topology and differential structure of the spacetime manifold as well as about the background metric to be approximated is supplied by coherent states. Given such data, the corresponding coherent state defines a sector in the Hilbert space of AQG which can be identified with a usual QFT on the given manifold and background. In particular, we show that AQG admits a semiclassical limit whose infinitesimal gauge symmetry agrees with that of General Relativity. (orig.)