Testing the master constraint programme for loop quantum gravity: III. models

@article{Dittrich2004TestingTM,
  title={Testing the master constraint programme for loop quantum gravity: III. 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… 
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 : 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
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 for Loop Quantum Gravity from Parametrised Field Theory
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
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
Flux formulation of loop quantum gravity: Classical framework
We recently introduced a new representation for loop quantum gravity (LQG), which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper
Algebraic quantum gravity (AQG): III. Semiclassical perturbation theory
In the two previous papers of this series we defined a new combinatorial approach to quantum gravity, algebraic quantum gravity (AQG). We showed that AQG reproduces the correct infinitesimal dynamics
Emergent diffeomorphism invariance in a discrete loop quantum gravity model
Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first-class algebra of
Quantum gravity kinematics from extended TQFTs
In this paper, we show how extended topological quantum field theories (TQFTs) can be used to obtain a kinematical setup for quantum gravity, i.e. a kinematical Hilbert space together with a
Master constraint operators in loop quantum gravity
...
...

References

SHOWING 1-10 OF 59 REFERENCES
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 : 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
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
Testing the master constraint programme for loop quantum gravity: IV. Free field theories
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: 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
Quantum spin dynamics (QSD): IV. ? Euclidean quantum gravity as a model to test ? Lorentzian quantum gravity
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
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
Quantum spin dynamics (QSD): VII. Symplectic structures and continuum lattice formulations of gauge field theories
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.
Quantization of Constrained Systems
TLDR
The quantization of systems with general first- and second-class constraints from the point of view of coherentstate, phase-space path integration is studied, and it is shown that all such cases may be treated by using suitable path-integral measures for the Lagrange multipliers which ensure that the quantum system satisfies the appropriate quantum constraint conditions.
Relational time in generally covariant quantum systems: four models
We analyze the relational quantum evolution of generally covariant systems in terms of Rovelli's evolving constants of motion and the generalized Heisenberg picture. In order to have a well-defined
...
...