PSI 2017/2018 - Quantum Gravity (Dupuis)

 Introduction and quick overview on Loop Quantum Cosmology.

Hamiltonian analysis of constrained systems.

Canonical analysis of the parametrized particle - The Dirac quantization program.

Dirac quantization of the parametrized particle - 3D gravity.

First order formulation of 3D gravity - Canonical analysis.

Canonical analysis of 3D gravity first order action - Interpretation of constraints - Constraint algebra.

Choice of basic variables - Configuration variables: holonomies.

Conjugated variables: fluxes - Poisson algebra

Kinematical Hilbert space for one edge - Length operator. 

Kinematical Hilbert space for a graph - Gauss constraint - spinnetwork states.

Flatness constraint - Physical Hilbert space.

4D Loop Quantum Gravity.