# A new look at Lorentz-Covariant Loop Quantum Gravity

@article{Geiller2011ANL,
title={A new look at Lorentz-Covariant Loop Quantum Gravity},
author={Marc Geiller and Marc Lachi{\e}ze‐Rey and Karim Noui},
journal={Physical Review D},
year={2011},
volume={84},
pages={044002}
}`
• Published 20 May 2011
• Physics
• Physical Review D
In this work, we study the classical and quantum properties of the unique commutative Lorentz-covariant connection for loop quantum gravity. This connection has been found after solving the second-class constraints inherited from the canonical analysis of the Holst action without the time-gauge. We show that it has the property of lying in the conjugacy class of a pure $\su(2)$ connection, a result which enables one to construct the kinematical Hilbert space of the Lorentz-covariant theory in…
32 Citations
A Lorentz-Covariant Connection for Canonical Gravity
• Physics
• 2011
We construct a Lorentz-covariant connection in the context of first order cano- nical gravity with non-vanishing Barbero{Immirzi parameter. To do so, we start with the phase space formulation derived
Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter
• Physics, Mathematics
• 2012
We perform the Lorentz-covariant Hamiltonian analysis of two Lagrangian action principles that describe general relativity as a constrained BF theory and that include the Immirzi parameter. The
Twistorial structure of loop-gravity transition amplitudes
• Physics
• 2012
The spin foam formalism provides transition amplitudes for loop quantum gravity. Important aspects of the dynamics are understood, but many open questions are pressing on. In this paper we address
Edge modes of gravity. Part II. Corner metric and Lorentz charges
• Physics, Mathematics
• 2020
In this second paper of the series we continue to spell out a new program for quantum gravity, grounded in the notion of corner symmetry algebra and its representations. Here we focus on tetrad
Testing the role of the Barbero-Immirzi parameter and the choice of connection in Loop Quantum Gravity
• Physics
• 2015
We study the role of the Barbero-Immirzi parameter $\gamma$ and the choice of connection in the construction of (a symmetry-reduced version of) loop quantum gravity. We start with the
Revisiting the solution of the second-class constraints of the Holst action
• Physics
Physical Review D
• 2019
In this paper we revisit the nonmanifestly Lorentz-covariant canonical analysis of the Holst action with a cosmological constant. We take a viewpoint close to that of F. Cianfrani and G. Montani
The Thiemann Complexifier and the CVH algebra for Classical and Quantum FLRW Cosmology
• Mathematics
• 2017
In the context of Loop Quantum Gravity (LQG), we study the fate of Thiemann complexifier in homogeneous and isotropic FRW cosmology. The complexifier is the dilatation operator acting on the
Gravity as an SU(1,1) gauge theory in four dimensions
• Mathematics, Physics
• 2017
We start with the Hamiltonian formulation of the first order action of pure gravity with a full $\mathfrak{sl}(2, \mathbb C)$ internal gauge symmetry. We make a partial gauge-fixing which reduces
Spin Foams and Canonical Quantization
• Physics
• 2012
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the
Manifestly Lorentz-covariant variables for the phase space of general relativity
• Physics
• 2018
We present a manifestly Lorentz-covariant description of the phase space of general relativity with the Immirzi parameter. This formulation emerges after solving the second-class constraints arising

## References

SHOWING 1-10 OF 29 REFERENCES
SU(2) loop quantum gravity seen from covariant theory
• Physics
• 2003
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).
Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras
• Mathematics
• 2006
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac:
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
Lorentz covariance of loop quantum gravity
• Physics
• 2011
The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where
Quantum theory of geometry: I. Area operators
• Mathematics
• 1996
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
Introduction to Modern Canonical Quantum General Relativity
This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the
Quantization of Gauge Systems
• Physics
• 1992
This is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical
Quantum geometry of isolated horizons and black hole entropy
• Physics
• 2000
Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting
Area spectrum in Lorentz covariant loop gravity
• Mathematics
• 2001
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