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

@article{Dittrich2004TestingTM, title={Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models}, author={Bianca Dittrich and Thomas Thiemann}, journal={Classical and Quantum Gravity}, year={2004}, volume={23}, pages={1089-1120} }

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, despite the fact that the phase space is finite dimensional, are much more complicated than in the second paper. These are systems with an gauge symmetry and the complications arise because non-compact semisimple Lie groups are not amenable (have no finite translation invariant measure). This leads…

## 58 Citations

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

- Computer Science
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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.

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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…

ul 2 00 5 Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity

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The volume operator plays a pivotal role for the quantum dynamics of Loop Quantum Gravity (LQG). It is essential in order to construct Triad operators that enter the Hamiltonian constraint and which…

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We investigate refined algebraic quantisation with group averaging in a constrained Hamiltonian system whose gauge group is the connected component of the lower triangular subgroup of SL(2,R). The…

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## References

SHOWING 1-10 OF 61 REFERENCES

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 : 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…

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: 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…

Quantum spin dynamics (QSD): IV. ? Euclidean quantum gravity as a model to test ? Lorentzian quantum gravity

- Physics
- 1997

The quantization of Lorentzian or Euclidean 2 + 1 gravity by canonical methods is a well studied problem. However, the constraints of 2 + 1 gravity are those of a topological field theory and…

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…

SL(2,R) model with two Hamiltonian constraints

- Physics
- 1999

We describe a simple dynamical model characterized by the presence of two noncommuting Hamiltonian constraints. This feature mimics the constraint structure of general relativity, where there is one…

Quantum spin dynamics (QSD): VII. Symplectic structures and continuum lattice formulations of gauge field theories

- Mathematics
- 2001

Interesting nonlinear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator-valued distributions.…