Seminarium Teorii Względności i Grawitacji

In this talk we introduce an approach called reduced phase space quantization. It uses the relational formalism introduced by Rovelli and further developed by Dittrich which is a concept to construct observables for constrained systems such as General Relativity. This approach can be combined with the Brown-Kuchar mechanism by means of which a so called physical Hamiltonian generating the evolution of those observables can be derived. Instead of solving the constraints on the quantum level by means of Dirac quantization reduced phase space quantization allows to directly quantize the algebra of observables as well as the physical Hamiltonian. We apply reduced phase space quantization to standard LQG as well as to the recently introduced framework of Algebraic Quantum Gravity and discuss their differences.