A Path-integral for the Master Constraint of Loop Quantum Gravity

Understand

In the present paper, we start from the canonical theory of loop quantum gravity and the master constraint programme.

• The physical inner product is expressed by using the group averaging technique for a single self-adjoint master constraint operator.
• By the standard technique of skeletonization and the coherent state path-integral, we derive a path-integral formula from the group averaging for the master constraint operator.
• Our derivation in the present paper suggests there exists a direct link connecting the canonical Loop quantum gravity with a path-integral quantization or a spin-foam model of General Relativity.