PSI 2018/2019 - Explorations in Quantum Gravity (Dupuis)

Introduction and overview by Bianca Dittrich on the different quantum gravity approaches.

Constrained systems and Hamiltonian formalism; gauge symmetries.

Example of the parametrized particle: Canonical analysis - Physical phase space and Dirac observables. The Dirac program: the program - case of the parametrized particle.

Actions for gravity: the Einstein-Hilbert action  - 3D gravity - first order formalism of 3D gravity (triads and connections)

First order formalism of 3D gravity: action and symmetries. Cannonical analysis.

Interpretation of the constraints - Constraint algebra

Dirac quantization of 3D gravity: basic variables, holonomy and flux.

Kinematical Hibert space for a subsystem: edge

Kinematical Hibert space for a subsystem: edge; length operator; Kinematical Hilbert space for a graph.

The Gauss constraint - spinnetwork states

The Flatness constraint - the physical Hibert space

Black hole perturbation theory