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

## TL;DR

This paper derives a path-integral formulation for the master constraint in loop quantum gravity, linking canonical quantization with path-integral and spin-foam approaches, potentially advancing the understanding of quantum gravity.

## Contribution

It introduces a path-integral formula for the master constraint in loop quantum gravity using group averaging and coherent states, establishing a connection to spin-foam models.

## Key findings

- Derived a path-integral expression from the master constraint
- Linked canonical loop quantum gravity to spin-foam models
- Provided a new framework for quantizing gravity

## Abstract

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.