New variables for classical and quantum gravity in all dimensions: III. Quantum theory

@article{Bodendorfer2011NewVF,
  title={New variables for classical and quantum gravity in all dimensions: III. Quantum theory},
  author={Norbert Bodendorfer and Thomas Thiemann and A. Thurn},
  journal={Classical and Quantum Gravity},
  year={2011},
  volume={30}
}
We quantize the new connection formulation of (D + 1)-dimensional general relativity developed in our companion papers by loop quantum gravity (LQG) methods. It turns out that all the tools prepared for LQG straightforwardly generalize to the new connection formulation in higher dimensions. The only new challenge is the simplicity constraint. While its ‘diagonal’ components acting at edges of spin-network functions are easily solved, its ‘off-diagonal’ components acting at vertices are non… 
View on IOP Publishing
arxiv.org
76 Citations
Highly Influential Citations
2
Background Citations
25
Methods Citations
13
Results Citations
2

76 Citations

New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis
Loop quantum gravity (LQG) relies heavily on a connection formulation of general relativity such that (1) the connection Poisson commutes with itself and (2) the corresponding gauge group is compact.…
From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in…
New variables for classical and quantum gravity in all dimensions: IV. Matter coupling
We employ the techniques introduced in the companion papers (Bodendorfer et al 2011 arXiv:1105.3703 [gr-qc]; arXiv:1105.3704 [gr-qc]; arXiv:1105.3705 [gr-qc]) to derive a connection formulation of…
New Hamiltonian constraint operator for loop quantum gravity
New variables for classical and quantum (super)-gravity in all dimensions
Supergravity was originally introduced in the hope of finding a theory of gravity without the shortcoming of perturbative non-renormalisability. Although this goal does not seem to have been reached…
New variables for classical and quantum gravity in all dimensions: V. Isolated horizon boundary degrees of freedom
In this paper, we generalize the treatment of isolated horizons in loop quantum gravity, resulting in a Chern–Simons theory on the boundary in the four-dimensional case, to non-distorted isolated…
Loop Quantum Cosmology, Modified Gravity and Extra Dimensions
Loop quantum cosmology (LQC) is a framework of quantum cosmology based on the quantization of symmetry reduced models following the quantization techniques of loop quantum gravity (LQG). This paper…
Wald entropy formula and loop quantum gravity
We outline how the Wald entropy formula naturally arises in loop quantum gravity based on recently introduced dimension-independent connection variables. The key observation is that in a loop…
Loop Quantum Gravity
This article presents an "in-a-nutshell" yet self-contained introductory review on loop quantum gravity (LQG) -- a background-independent, nonperturbative approach to a consistent quantum theory of…
Loop quantum gravity and cosmological constant
...
...

References

SHOWING 1-10 OF 51 REFERENCES
New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis
Loop quantum gravity (LQG) relies heavily on a connection formulation of general relativity such that (1) the connection Poisson commutes with itself and (2) the corresponding gauge group is compact.…
New variables for classical and quantum gravity in all dimensions: IV. Matter coupling
We employ the techniques introduced in the companion papers (Bodendorfer et al 2011 arXiv:1105.3703 [gr-qc]; arXiv:1105.3704 [gr-qc]; arXiv:1105.3705 [gr-qc]) to derive a connection formulation of…
New variables for classical and quantum (super)-gravity in all dimensions
Supergravity was originally introduced in the hope of finding a theory of gravity without the shortcoming of perturbative non-renormalisability. Although this goal does not seem to have been reached…
Loop-quantum-gravity vertex amplitude.
TLDR
This work presents an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly.
Spin networks and quantum gravity.
  • RovelliSmolin
  • Physics
    Physical review. D, Particles and fields
  • 1995
TLDR
A new basis on the state space of non-perturbative quantum gravity is introduced that allows a simple expression for the exact solutions of the Hamiltonian constraint (Wheeler-DeWitt equation) that have been discovered in the loop representation.
New spinfoam vertex for quantum gravity
We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the…
Closed formula for the matrix elements of the volume operator in canonical quantum gravity
We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four space–time dimensions in the continuum in a spin-network basis. We also…
New variables for classical and quantum gravity in all dimensions: II. Lagrangian analysis
We rederive the results of our companion paper, for matching space–time and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the…
Towards loop quantum supergravity (LQSG): II. p-form sector
In our companion paper, we focused on the quantization of the Rarita–Schwinger sector of supergravity theories in various dimensions by using an extension of loop quantum gravity to all spacetime…
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…
...
...