# Testing the Master Constraint Programme for Loop Quantum Gravity I. General Framework

@article{Dittrich2004TestingTM, title={Testing the Master Constraint Programme for Loop Quantum Gravity I. General Framework}, author={Bianca Dittrich and Thomas Thiemann}, journal={Classical and Quantum Gravity}, year={2004}, volume={23}, pages={1025-1065} }

Recently, the master constraint programme for loop quantum gravity (LQG) was proposed as a classically equivalent way to impose the infinite number of Wheeler?DeWitt constraint equations in terms of a single master equation. While the proposal has some promising abstract features, it was until now barely tested in known models. In this series of five papers we fill this gap, thereby adding confidence to the proposal. We consider a wide range of models with increasingly more complicated…

## 90 Citations

Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models

- Mathematics
- 2004

This is the third 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 analyse models which,…

The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity

- Physics
- 2006

The Hamiltonian constraint remains the major unsolved problem in loop quantum gravity (LQG). Some time ago, a mathematically consistent candidate Hamiltonian constraint was proposed but there are…

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…

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…

- qc / 0 51 00 11 v 1 4 O ct 2 00 5 Quantum Spin Dynamics VIII . The Master Constraint

- Mathematics
- 2008

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…

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…

Lessons for Loop Quantum Gravity from Parametrised Field Theory

- Mathematics
- 2010

In a series of seminal papers, Laddha and Varadarajan have developed in depth the quantisation of Parametrised Field Theory (PFT) in the kind of discontinuous representations that are employed in…

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…

## References

SHOWING 1-10 OF 59 REFERENCES

Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models

- Mathematics
- 2004

This is the third 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 analyse models which,…

The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity

- Physics
- 2006

The Hamiltonian constraint remains the major unsolved problem in loop quantum gravity (LQG). Some time ago, a mathematically consistent candidate Hamiltonian constraint was proposed but there are…

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…

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: 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…

QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories

- Physics
- 1997

It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague…

Reduced phase space quantization and Dirac observables

- Mathematics
- 2006

In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint…

Quantum spin dynamics (QSD) V: Quantum Gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories

- Physics
- 1998

It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague…

QSD III : Quantum Constraint Algebra and Physical Scalar Product in Quantum General Relativity

- Mathematics
- 1997

This paper deals with several technical issues of non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum that arose in connection with the recently constructed…