Hamburg 2016 – scientific programme

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GR: Fachverband Gravitation und Relativitätstheorie

GR 2: Quantum Gravity I

GR 2.3: Talk

Monday, February 29, 2016, 12:00–12:20, VMP6 HS A

A physical Hamiltonian obtained from four Klein-Gordon Fields — Kristina Giesel and •Almut Oelmann — Institute for Quantum Gravity, FAU Erlangen-Nürnberg

In Loop Quantum Gravity (LQG) we do not have a true Hamiltonian which describes the dynamics of General Relativity. Instead one obtains from the Einstein-Hilbert action a sum of constraints, called the Diffeomorphism and the Hamiltonian constraint. They represent spatial and temporal diffeomorphisms which are the gauge transformations of General Relativity. In order to obtain Dirac observables which are real physical (gauge invariant) quantities one introduces additional matter fields as reference fields. A special Dirac observable is the physical Hamiltonian. It describes the physical evolution (dynamics) of the considered system. A well known approach to obtain Dirac observables that are invariant under spatial and temporal diffeomorphisms is the so called relational formalism combined with the so called Brown-Kuchar mechanism, where four dust fields are used as reference fields. Here we consider the model of the gravitational field coupled to four Klein-Gordon reference fields and derive the physical Hamiltonian of this model. We compare this model to the Brown-Kuchar dust model and discuss the differences and similarities of the two models with a particular focus on the reduced phase space quantization of this model in the context of Loop Quantum Gravity.