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

@article{Dittrich2006TestingTM, title={Testing the master constraint programme for loop quantum gravity: II. Finite-dimensional systems}, author={Bianca Dittrich and Thomas Thiemann}, journal={Classical and Quantum Gravity}, year={2006}, volume={23}, pages={1067-1088} }

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 simplest examples: finite-dimensional models with a finite number of first or second class constraints, Abelian or non-Abelian, with or without structure functions.

## 62 Citations

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

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

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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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- 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…

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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…

Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity II

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- 2005

In this paper, we provide the techniques and proofs for the results presented in our companion paper concerning the consistency check on volume and triad operator quantization in loop quantum gravity.

Loop quantum gravity - a short review

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In this article we review the foundations and the present status of loop quantum gravity. It is short and relatively non-technical, the emphasis is on the ideas, and the flavor of the techniques. In…

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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…

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

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- 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.

Quantum spin dynamics: VIII. The master constraint

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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…

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