# 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} }

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.

## 27 Citations

### Solving the simplicity constraints for spinfoam quantum gravity

- Physics
- 2007

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

- Physics
- 2007

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

- Physics
- 2009

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

- Mathematics
- 2008

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

- Physics
- 2008

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

- Physics
- 2018

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

- Physics
- 2008

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

- Physics
- 2011

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

- Physics
- 2011

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

- Physics
- 2008

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…

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