# A path integral for the master constraint of loop quantum gravity

@article{Han2010API, title={A path integral for the master constraint of loop quantum gravity}, author={Muxin Han}, journal={Classical and Quantum Gravity}, year={2010}, volume={27}, pages={215009} }

In the present paper, we start from the canonical theory of loop quantum gravity and the master constraint program. 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 this paper suggests there exists a direct link…

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## References

SHOWING 1-10 OF 69 REFERENCES

Testing the master constraint programme for loop quantum gravity: IV. Free field theories

- Physics, Geology
- 2006

This is the fourth paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. We now move on to free field theories…

Testing the master constraint programme for loop quantum gravity : V. Interacting field theories

- Physics
- 2006

This is the fifth and final paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. Here we consider interacting…

Quantum spin dynamics: VIII. The master constraint

- Mathematics
- 2006

Recently the master constraint programme (MCP) for loop quantum gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single master constraint. The MCP is…

Loop-quantum-gravity vertex amplitude.

- PhysicsPhysical review letters
- 2007

This work presents an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly.

Testing the master constraint programme for loop quantum gravity: II. Finite-dimensional systems

- Physics
- 2006

This is the second paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. In this work, we begin with the…

On the relation between operator constraint, master constraint, reduced phase space and path integral quantization

- Physics
- 2010

Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space…

FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY

- Physics
- 2007

In the recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is…

New variables for classical and quantum gravity.

- PhysicsPhysical review letters
- 1986

A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced that enables one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory.

Canonical Path-Integral Measures for Holst and Plebanski Gravity. II. Gauge Invariance and Physical Inner Product

- Physics
- 2009

This paper serves as a continuation for the discussion in Engle et al (2010, Class. Quantum Grav. 27 245014). We analyze the invariance properties of the gravity path-integral measure derived from…