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… 
View PDF on arXiv
49 Citations
Background Citations
4
Methods Citations
6

49 Citations

Citation Type

Citation Type

Testing the master constraint programme for loop quantum gravity: II. Finite-dimensional systems
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
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
TLDR
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
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,…
Master constraint operators in loop quantum gravity
A path integral for the master constraint of loop quantum gravity
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
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
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
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
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
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
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
TLDR
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
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
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…
Universal procedure for enforcing quantum constraints
Quantum spin dynamics (QSD) V: Quantum Gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories
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
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
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…
Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
...
...