Applied Mathematics, University of Waterloo
Time Gauge Fixing in 3d Loop Quantum Gravity
Loop quantum gravity is a non-perturbative and background independent approach to the quantization of general relativity. It predicts the discreteness of geometrical operators like the area and the volume of spacetime. In the more physical 4-dimensional case of loop quantum gravity, a time gauge is introduced to construct the Ashtekar-Barbero variables. This provides a sure way to obtain a phase space parametrized by a connection and its conjugate momentum. Mimicking this concept, a particular time gauge will be implemented in the 3-dimensional loop quantum gravity case. This will be the focus of this talk. I will look at the results obtained so far, the challenges and the way forward. In addition, the relevant issues of dynamics and kinematics of loop quantum gravity will also be presented.