PSI 2016/2017 - Explorations in Quantum Gravity (Dupuis)

Introduction and a short section on Black Hole in Loop Quantum Gravity by an invited speaker, Eugenio Bianchi.

4D Einstein-Hilbert action and equations of motion - 3D gravity - Towards the first order action for 3D gravity: triads and connection.

Spin connection - The first order action for 3D gravity - Hamiltonian formulation of constrained systems and symmetries.

Hamiltonian formulation of constrained systems: examples from tutorial 1; notions of primary, secondary... constraints and notions of first class and second class constraints - Relation constraints/gauge symmetries - A totally constrained system: the parametrized particle.

The parametrized particle: notion of Dirac observables - Canonical analysis of the first order action for 3D gravity - Constraints of 3D gravity (1st order formulation): Gauss constraints and Flatness constraints.

Interpretation of the constraints and symmetries of the first order action for 3D gravity - Constraint algebra - The Dirac program applied to the parametrized particle.

1st step of the Dirac program applied to the first order action for 3D gravity, choice of the basic variables: holonomies.

The flux variables - The holonomy-flux algebra.

Quantization of one edge (subsystem).

Length operator - Introduction to Loop Quantum Cosmology (video by Aurélien Barrau).

Gauss constraint - Intertwiners

Spinnetwork states - Flatness constraint - Physical state.