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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References
SHOWING 1-10 OF 140 REFERENCES
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 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,…
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: 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…
QSD III : Quantum Constraint Algebra and Physical Scalar Product in Quantum General Relativity
- Mathematics
- 1997
This paper deals with several technical issues of non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum that arose in connection with the recently constructed…
Loop Quantum Cosmology
- PhysicsLiving reviews in relativity
- 2005
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities,…
A lattice approach to spinorial quantum gravity
- Physics
- 1989
The authors present a new lattice regularisation of quantum general relativity based on Ashtekar's reformulation (1986) of Hamiltonian general relativity. In this form, quantum states of the…
Loop quantum cosmology: I. Kinematics
- Physics
- 2000
The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows us to test loop quantum gravity in a large class of…
The classical limit and the form of the hamiltonian constraint in nonperturbative quantum gravity
- Physics
- 1996
It is argued that some approaches to non-perturbative quantum general relativity lack a sensible continuum limit that reproduces general relativity. The basic problem is that generic physical states…