# The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity

@article{Thiemann2006ThePP, title={The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity}, author={Thomas Thiemann}, journal={Classical and Quantum Gravity}, year={2006}, volume={23}, pages={2211-2247} }

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 still several unsettled questions which concern the algebra of commutators among smeared Hamiltonian constraints which must be faced in order to make progress. In this paper, we propose a solution to this set of problems based on the so-called master constraint which combines the smeared Hamiltonian…

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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…

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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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,…

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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…

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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…

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