• Corpus ID: 118268224

Towards a Covariant Loop Quantum Gravity

@article{Livine2006TowardsAC,
  title={Towards a Covariant Loop Quantum Gravity},
  author={Etera R. Livine},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2006}
}
  • E. Livine
  • Published 30 August 2006
  • Physics
  • arXiv: General Relativity and Quantum Cosmology
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 and leads to a theory of Covariant Loop Quantum Gravity. This new formulation does not suffer from the Immirzi ambiguity, it has a continuous area spectrum and uses spin networks for the Lorentz group. Finally, its dynamics can easily be related to Barrett-Crane like spin foam models. 

Solving the simplicity constraints for spinfoam quantum gravity

General relativity can be written as topological BF theory plus a set of second-class constraints. Classically the constraints provide the geometric interpretation of the B variables and reduce BF to

Plebanski theory and covariant canonical formulation

We establish an equivalence between the Hamiltonian formulation of the Plebanski action for general relativity and the covariant canonical formulation of the Hilbert–Palatini action. This is done by

Matter in loop quantum gravity without time gauge: A nonminimally coupled scalar field

We analyze the phase space of gravity nonminimally coupled to a scalar field in a generic local Lorentz frame. We reduce the set of constraints to a first class one by fixing a specific hypersurfaces

A new perspective on covariant canonical gravity

We present a new approach to the covariant canonical formulation of Einstein–Cartan gravity that preserves the full Lorentz group as the local gauge group. The method exploits lessons learned from

A Immirzi-like parameter for 3D quantum gravity

We study an Immirzi-like ambiguity in three-dimensional quantum gravity. It shares some features with the Immirzi parameter of four-dimensional loop quantum gravity: it does not affect the equations

Quasi-Hopf Symmetry in Loop Quantum Gravity with Cosmological constant and Spinfoams with timelike surfaces

In this thesis we study two separate problems concerning improvements to the Loop quantum gravity and spinfoam approach to quantum gravity. In the first part we address the question about the origin

Spin foam model from canonical quantization

We suggest a modification of the Barrett-Crane spin foam model of four-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop

Spin Foam Models for Quantum Gravity and semi-classical limit

The spinfoam framework is a proposal for a regularized path integral for quantum gravity. Spinfoams define quantum space-time structures describing the evolution in time of the spin network states

A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity

This is my Th\`ese d'Habilitation (HDR) on the topic of spinfoam models for quantum gravity, which I presented in l'Ecole Normale Sup\'erieure de Lyon on december 16 2010. The spinfoam framework is a

Canonical Lagrangian dynamics and general relativity

Building towards a more covariant approach to canonical classical and quantum gravity we outline an approach to constrained dynamics that de-emphasizes the role of the Hamiltonian phase space and

References

SHOWING 1-10 OF 26 REFERENCES

Area spectrum in Lorentz covariant loop gravity

We use the manifestly Lorentz covariant canonical formalism to evaluate eigenvalues of the area operator acting on Wilson lines. To this end we modify the standard definition of the loop states to

On choice of connection in loop quantum gravity

We investigate the quantum area operator in the loop approach based on the Lorentz covariant Hamiltonian formulation of general relativity. We show that there exists a two-parameter family of Lorentz

SU(2) loop quantum gravity seen from covariant theory

Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints (“simplicity” constraints).

Projected spin networks for Lorentz connection: linking spin foams and loop gravity

In the search for a covariant formulation for loop quantum gravity, spin foams have arisen as the corresponding discrete spacetime structure and, among the different models, the Barrett–Crane model

Canonical quantization of a minisuperspace model for gravity using self-dual variables

The present article summarizes the work of the papers \cite{1} dealing with the quantization of pure gravity and gravity coupled to a Maxwell field and a cosmological constant in presence of

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

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

Timelike surfaces in Lorentz covariant loop gravity and spin foam models

We apply a recently developed canonical formulation of general relativity, which possesses explicit covariance with respect to Lorentz transformations in the tangent space, to describe the case of a

Barrett-Crane spin foam model from generalized BF-type action for gravity

We study a generalized action for gravity as a constrained BF theory, and its relationship with the Plebanski action. We analyse the discretization of the constraints and the spin foam quantization

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

Implementing causality in the spin foam quantum geometry