11* - Canonical formalism for gravity, the Wheeler–de Witt equation, and the canonical quantization of gravity

Summary

We define the canonical formalism for gravity. After a quick review of the Dirac formalism for constrained systems, we use it for gravity, and find the Hamiltonian constraint and the momentum constraint. We use them for defining the Wheeler–de Witt equation, the quantum version of the Einstein equations, and their solution, the wave function of the Universe, in the Hawking “no-boundary boundary condition” and the Villenkin “tunneling from nothing” versions, with their corresponding interpretations. We also define the Brown–York stress tensor in AdS background. Finally, we define Ashtekar variables, and the corresponding quantization in Dirac formalism for canonical gravity.