Loop Quantization of Shape Dynamics

Understand

Loop Quantum Gravity (LQG) is a promising approach to quantum gravity, in particular because it is based on a rigorous quantization of the kinematics of gravity.

• A difficult and still open problem in the LQG program is the construction of the physical Hilbert space for pure quantum gravity.
• This is due to the complicated nature of the Hamilton constraints.
• The Shape Dynamics description of General Relativity (GR) replaces the Hamilton constraints with spatial Weyl constraints, so the problem of finding the physical Hilbert space reduces to the problem of quantizing the Weyl constraints.