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

@article{Dittrich2006TestingTM, title={Testing the master constraint programme for loop quantum gravity: IV. Free field theories}, author={Bianca Dittrich and Thomas Thiemann}, journal={Classical and Quantum Gravity}, year={2006}, volume={23}, pages={1121-1142} }

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 with constraints, namely Maxwell theory and linearized gravity. Since the master constraint involves squares of constraint operator valued distributions, one has to be very careful in doing that and we will see that the full flexibility of the master constraint programme must be exploited in order to…

## 49 Citations

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…

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…

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

- Computer Science
- 2004

It is shown that the master constraint programme has a wide range of applicability but that there are many, physically interesting subtleties that must be taken care of in doing so.

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,…

A path integral for the master constraint of loop quantum gravity

- Physics
- 2010

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…

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…

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…

Lessons from toy-models for the dynamics of loop quantum gravity

- Physics
- 2012

We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of…

An elementary introduction to loop quantum gravity

- Physics
- 2016

An introduction to loop quantum gravity is given, focussing on the fundamental aspects of the theory, different approaches to the dynamics, as well as possible future directions. It is structured in…

## References

SHOWING 1-10 OF 49 REFERENCES

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…

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…

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

- Computer Science
- 2004

It is shown that the master constraint programme has a wide range of applicability but that there are many, physically interesting subtleties that must be taken care of in doing so.

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…

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…

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 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…

An invitation to loop quantum gravity

- Physics
- 2004

We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one…