T. Daniel - Canonical Quantization of Gravity and the Wheeler-DeWitt Equation

This is a talk that was given in the Rutgers Graduate/Undergraduate Online Seminar in Mathematical Physics (GUOSIMP). We host talks every other week on Thursdays from 12:10pm to 1:10pm EST. Speaker: Tatsuya Daniel (Brown) Date: Dec 1st, 2022 Title: Canonical Quantization of Gravity and the Wheeler-DeWitt Equation Abstract: The Kodama state is a candidate for describing quantum gravity non-perturbatively upon canonically quantizing the Hamiltonian formulation of General Relativity (GR) with a positive cosmological constant; however, it suffers from a number of issues, including non-normalizability, its CPT-violating properties, as well as lack of gauge invariance under large gauge transformations. In the first part of this two-talk series, I will review first and second quantization before introducing the canonical formulation of GR. I will show how the Wheeler-DeWitt equation emerges as a constraint upon the quantization of GR in this Hamiltonian formalism. The Kodama state is the exact solution to the Wheeler-DeWitt equation when written in terms of the so-called Ashtekar variables, which I will discuss more in the second talk.