Spectra of length and area in (2 + 1) Lorentzian loop quantum gravity

@article{Freidel2003SpectraOL,
  title={Spectra of length and area in (2 + 1) Lorentzian loop quantum gravity},
  author={Laurent Freidel and Etera R. Livine and Carlo Rovelli},
  journal={Classical and Quantum Gravity},
  year={2003},
  volume={20},
  pages={1463-1478}
}
We study the spectrum of the length and area operators in Lorentzian loop quantum gravity, in 2 + 1 spacetime dimensions. We find that the spectrum of spacelike intervals is continuous, whereas the spectrum of timelike intervals is discrete. This result contradicts the expectation that spacelike intervals are always discrete. On the other hand, it is consistent with the results of the spin foam quantization of the same theory. 
Loop quantum cosmology in 2+1 dimension
As a first step to generalize the structure of loop quantum cosmology to the theories with the spacetime dimension other than four, the isotropic model of loop quantum cosmology in 2+1 dimension is
In search of fundamental discreteness in (2 + 1)-dimensional quantum gravity
Inspired by previous work in (2 + 1)-dimensional quantum gravity, which found evidence for a discretization of time in the quantum theory, we reexamine the issue for the case of pure Lorentzian
Spectra of geometric operators in three-dimensional loop quantum gravity: From discrete to continuous
We study and compare the spectra of geometric operators (length and area) in the quantum kinematics of two formulations of three-dimensional Lorentzian loop quantum gravity. In the SU(2)
Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
  • S. Carlip
  • Physics
    Living reviews in relativity
  • 2005
TLDR
A summary of the rather large body of work that has gone towards quantizing (2 + 1)-dimensional vacuum gravity in the setting of a spatially closed universe is summarized.
Towards a Covariant Loop Quantum Gravity
We review the canonical analysis of the Palatini action without going to the time gauge as in the standard derivation of Loop Quantum Gravity. This allows to keep track of the Lorentz gauge symmetry
Time level splitting in quantum Chern–Simons gravity
Using the Dirac theory of constraints, the reduction procedure for the field degrees of freedom, the number of which is restricted by the equations of motion and topological conditions, is proposed.
The Matrix Elements of Area Operator in (2+1) Euclidean Loop Quantum Gravity
In this article we discuss the matrix elements of area operator in (2+1) Euclidean Loop Quantum Gravity. The Euclidean signature is chosen because it has the same group as (3+1) Lorentzian Loop
Abelian 2+1D loop quantum gravity coupled to a scalar field
  • C. Charles
  • Physics
    General Relativity and Gravitation
  • 2019
In order to study 3d loop quantum gravity coupled to matter, we consider a simplified model of abelian quantum gravity, the so-called $$\mathrm {U}(1)^3$$U(1)3 model. Abelian gravity coupled to a
The Entropy of BTZ Black Hole from Loop Quantum Gravity
TLDR
The result that the horizon degrees of freedom can be described by the 2D SO(1,1) punctured BF theory is got and the area law for the entropy of BTZ black hole is got.
(2+1)-dimensional loop quantum cosmology of Bianchi I models
We study the anisotropic Bianchi I loop quantum cosmology in 2+1 dimensions. Both the $\mubar$ and $\mubar'$ schemes are considered in the present paper and the following expected results are
...
...

References

SHOWING 1-10 OF 31 REFERENCES
3+1 spinfoam model of quantum gravity with spacelike and timelike components
We present a spin foam formulation of Lorentzian quantum general relativity. The theory is based on a simple generalization of a Euclidean model defined in terms of a field theory over a group. The
Loop quantum gravity and quanta of space: a primer
We present a straightforward and self-contained introduction to the basics of the loop approach to quantum gravity, and a derivation of what is arguably its key result, namely the spectral analysis
Quasinormal modes, the area spectrum, and black hole entropy.
TLDR
A result from classical gravity concerning the quasinormal mode spectrum of a black hole is used to fix the Immirzi parameter and the Bekenstein-Hawking expression of A/4l(2)(P) for the entropy of ablack hole is arrived at.
A State Sum Model for (2+1) Lorentzian Quantum Gravity
A state sum model based on the group SU(1,1) is defined. Investigations of its geometry and asymptotics suggest it is a good candidate for modelling (2+1) Lorentzian quantum gravity.
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
Spin foam model for Lorentzian general relativity
We present a spin foam formulation of Lorentzian quantum General Relativity. The theory is based on a simple generalization of an Euclidean model defined in terms of a field theory over a group. Its
Knot theory and quantum gravity.
A new represenatation for quantum general relativity is described, which is defined in terms of functionals of sets of loops in three-space. In this representation exact solutions of the quantum
Loop Quantum Gravity
TLDR
A general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity is provided, and a guide to the relevant literature is provided.
Quantum theory of geometry: I. Area operators
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated
...
...