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

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

2009-11-17

arxiv.org/abs/0911.3432v2

Class.Quant.Grav.27:215009,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages

Scientific paper

10.1088/0264-9381/27/21/215009

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.

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