Lessons from toy-models for the dynamics of loop quantum gravity

@article{Bonzom2012LessonsFT,
  title={Lessons from toy-models for the dynamics of loop quantum gravity},
  author={Valentin Bonzom and Alok Laddha},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2012},
  volume={8},
  pages={009}
}
  • V. Bonzom, Alok Laddha
  • Published 10 October 2011
  • Physics
  • Symmetry Integrability and Geometry-methods and Applications
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 the quantum Hamiltonian is presented, and then more recent approaches. They are based on toy models which provide new insights into the difficulties and ambiguities faced in Thiemann's construction. The models we use are parametrized field theories, the topological BF model of which a special case is… 

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References

SHOWING 1-10 OF 131 REFERENCES
The Group field theory approach to quantum gravity
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local
A new look at loop quantum gravity
I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments in the past few years. I point out that a theory is now available, having a
Loop quantum gravity : an outside view
We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasize that the off-shell (‘strong’)
Quantum gravity in terms of topological observables
We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes
Introduction to loop quantum gravity and spin foams
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection
Linking covariant and canonical loop quantum gravity: New solutions to the Euclidean scalar constraint
It is often emphasized that spin-foam models could realize a projection on the physical Hilbert space of canonical Loop Quantum Gravity (LQG). As a first test we analyze the one-vertex expansion of a
Three-dimensional loop quantum gravity: physical scalar product and spin-foam models
In this paper, we address the problem of the dynamics in three-dimensional loop quantum gravity with zero cosmological constant. We construct a rigorous definition of Rovelli's generalized projection
On the regularization of the constraint algebra of quantum gravity in 2 + 1 dimensions with a nonvanishing cosmological constant
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three-dimensional (Riemannian) gravity with a positive cosmological constant (Λ > 0). We show that the
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
Pushing Further the Asymptotics of the 6j-symbol
In the context of spin-foam models for quantum gravity, we investigate the asymptotical behavior of the (6j)-symbol at next-to-leading order. This gives the first quantum gravity correction to the
...
...