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In the present paper, we start from the canonical theory of loop quantumgravity and the master constraint programme. The physical inner product isexpressed by using the group averaging technique for a single self-adjointmaster constraint operator. By the standard technique of skeletonization andthe coherent state path-integral, we derive a path-integral formula from thegroup averaging for the master constraint operator. Our derivation in thepresent paper suggests there exists a direct link connecting the canonical Loopquantum gravity with a path-integral quantization or a spin-foam model ofGeneral Relativity.

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