Etera R. Livine

The 6j-symbol: Recursion, Correlations and Asymptotics (2009)

We discuss the construction of a scalar field theory with momentum space given by a coset. By introducing a generalized Fourier transform, we show how the dual scalar field theory actually lives in...

Dupuis, Maite, Livine, Etera R.

We study the asymptotic expansion of the 6j-symbol using the Schulten-Gordon recursion relations. We focus on the particular case of the isosceles tetrahedron and we provide explicit formulas for up...

Sub-leading asymptotic behaviour of area correlations in the Barrett-Crane model (2009)

Christensen, J. Daniel, Khavkine, Igor, Livine, Etera R., Speziale, Simone

The Barrett-Crane spin foam model for quantum gravity provides an excellent setting for testing analytical and numerical tools used to probe spinfoam models. Here, we complete the report on the...

Notes on the Qubit Phase Space and Discrete Symplectic Structures (2009)

Pushing Further the Asymptotics of the 6j-symbol (2009)

We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite dimensional Hilbert spaces. We look at this framework from a...

Dupuis, Maite, Livine, Etera R.

In the context of spinfoam models for quantum gravity, we investigate the asymptotical behavior of the 6j-symbol at next-to-leading order. We compute it analytically and check our results against...

Holomorphic Factorization for a Quantum Tetrahedron (2009)

Freidel, Laurent, Krasnov, Kirill, Livine, Etera R.

We provide a holomorphic description of the Hilbert space H(j_1,..,j_n) of SU(2)-invariant tensors (intertwiners) and establish a holomorphically factorized formula for the decomposition of identity...

4d Deformed Special Relativity from Group Field Theories (2009)

Girelli, Florian, Livine, Etera R., Oriti, Daniele

We derive a scalar field theory of the deformed special relativity type, living on non-commutative kappa-Minkowski spacetime and with a kappa-deformed Poincare symmetry, from the SO(4,1) group field...

A Lagrangian approach to the Barrett-Crane spin foam model (2008)

Bonzom, Valentin, Livine, Etera R.

We provide the Barrett-Crane spin foam model for quantum gravity with a discrete action principle, consisting in the usual BF term with discretized simplicity constraints which in the continuum turn...

The non-commutative geometry of matrix models: the Spinfoam way (2008)

A Note on B-observables in Ponzano-Regge 3d Quantum Gravity (2008)

Group field theories provide a non-perturbative formulation of spin foam models for quantum gravity. Focusing on 2d group field theories, we review their explicit relation to matrix models and show...

Livine, Etera R., Ryan, James P.

We study the insertion and value of metric observables in the (discrete) path integral formulation of the Ponzano-Regge spinfoam model for 3d quantum gravity. In particular, we discuss the length...

The entropic boundary law in BF theory (2008)

Towards the graviton from spinfoams: the complete perturbative expansion of the 3d toy model (2008)

We compute the entropy of a closed bounded region of space for pure 3d Riemannian gravity formulated as a topological BF theory for the gauge group SU(2) and show its holographic behavior. More...

Bonzom, Valentin, Livine, Etera R., Smerlak, Matteo, Speziale, Simone

We consider an exact expression for the 6j-symbol for the isosceles tetrahedron, involving integrals over SU(2), and use it to write the two-point function of 3d gravity on a single tetrahedron as a...

A Immirzi-like parameter for 3d quantum gravity (2008)

Bonzom, Valentin, Livine, Etera R.

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...

Physical boundary state for the quantum tetrahedron (2007)

N=2 supersymmetric spin foams in three dimensions (2007)

We consider stability under evolution as a criterion to select a physical boundary state for the spinfoam formalism. As an example, we apply it to the simplest spinfoam defined by a single quantum...

Livine, Etera R., Ryan, James P.

We construct the spin foam model for N=2 supergravity in three dimensions. Classically, it is a BF theory with gauge algebra osp(2|2). This algebra has representations which are not completely...

Numerical evidence of regularized correlations in spin foam gravity (2007)

Christensen, J. Daniel, Livine, Etera R., Speziale, Simone

We report on the numerical analysis of the area correlations in spin foam gravity on a single 4-simplex considered by Rovelli in PRL 97 (2006) 151301. We compare the asymptotics and confirm the...

Some comments on the universal constant in DSR (2007)

Relativistic particle: Dirac observables and Feynman propagator (2007)

Deformed Special Relativity is usually presented as a deformation of Special Relativity accommodating a new universal constant, the Planck mass, while respecting the relativity principle. In order to...

Freidel, Laurent, Girelli, Florian, Livine, Etera R.

We analyze the algebra of Dirac observables of the relativistic particle in four space-time dimensions. We show that the position observables become non-commutative and the commutation relations lead...

Non-Commutativity of Effective Space-Time Coordinates and the Minimal Length (2007)

Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity (2007)

Considering that a position measurement can effectively involve a momentum-dependent shift and rescaling of the "true" space-time coordinates, we construct a set of effective space-time coordinates...

Bulk Entropy in Loop Quantum Gravity (2007)

We give an independent derivation of the Engle-Pereira-Rovelli spinfoam model for quantum gravity which recently appeared in [arXiv:0705.2388]. Using the coherent state techniques introduced earlier...

A new spinfoam vertex for quantum gravity (2007)

In the framework of loop quantum gravity (LQG), having quantum black holes in mind, we generalize the previous boundary state counting (gr-qc/0508085) to a full bulk state counting. After a suitable...

3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory (2007)

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...

Fairbairn, Winston, Livine, Etera R.

An effective field theory for matter coupled to three-dimensional quantum gravity was recently derived in the context of spinfoam models in hep-th/0512113. In this paper, we show how this relates to...

The Relativistic Particle: Dirac observables and Feynman propagator (2007)

Freidel, Laurent, Girelli, Florian, Livine, Etera R.

We analyze the algebra of Dirac observables of the relativistic particle in four space-time dimensions. We show that the position observables become non-commutative and the commutation relations lead...

Quantum causal histories in the light of quantum information (2007)

Livine, Etera R, Terno, Daniel R

We use techniques of quantum information theory to analyze the quantum causal histories approach to quantum gravity. While it is consistent to introduce closed timelike curves (CTCs), they cannot...

Some comments on the universal constant in DSR (2006)

Quantum causal histories in the light of quantum information (2006)

Deformed Special Relativity is usually presented as a deformation of Special Relativity accommodating a new universal constant, the Planck mass, while respecting the relativity principle. In order to...

Group Integral Techniques for the Spinfoam Graviton Propagator (2006)

We use techniques of quantum information theory to analyze the quantum causal histories approach to quantum gravity. We show that while it is consistent to introduce closed timelike curves (CTCs),...

Towards a Covariant Loop Quantum Gravity (2006)

We consider the proposal of gr-qc/0508124 for the extraction of the graviton propagator from the spinfoam formalism. We propose a new ansatz for the boundary state, using which we can write the...

Towards the graviton from spinfoams: higher order corrections in the 3d toy model (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...

Livine, Etera R., Speziale, Simone, Willis, Joshua L.

We consider the recent calculation gr-qc/0508124 of the graviton propagator in the spinfoam formalism. Within the 3d toy model introduced in gr-qc/0512102, we test how the spinfoam formalism can be...

Physics of Deformed Special Relativity: Relativity Principle Revisited (2006)

Florian Girelli, Etera R. Livine

Physics of Deformed Special Relativity: Relativity Principle Revisited

Some Remarks on the Semi-Classical Limit of Quantum Gravity (2006)

Etera R. Livine

Some Remarks on the Semi-Classical Limit of Quantum Gravity

Reconstructing Quantum Geometry from Quantum Information: Area Renormalisation, Coarse-Graining and Entanglement on Spin Networks (2006)

Quantum black holes : entropy and entanglement on the horizon (2006)

After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a...

Livine, Etera R, Terno, Daniel R

We are interested in black holes in Loop Quantum Gravity (LQG). We study the simple model of static black holes: the horizon is made of a given number of identical elementary surfaces and these small...

3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory (2005)

Freidel, Laurent, Livine, Etera R.

We show that the effective dynamics of matter fields coupled to 3d quantum gravity is described after integration over the gravitational degrees of freedom by a braided non-commutative quantum field...

Coupling of spacetime atoms and spin foam renormalisation from group field theory (2005)

SU(2) Loop Quantum Gravity seen from Covariant Theory (2005)

We study the issue of coupling among 4-simplices in the context of spin foam models obtained from a group field theory formalism. We construct a generalisation of the Barrett-Crane model in which an...

Quantum Black Holes: Entropy and Entanglement on the Horizon (2005)

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\'\'...

Physics of deformed special relativity: relativity principle revisited (2005)

We are interested in black holes in Loop Quantum Gravity (LQG). We study the simple model of static black holes: the horizon is made of a given number of identical elementary surfaces and these small...

Girelli,Florian, Livine,Etera R.

In many different ways, Deformed Special Relativity (DSR) has been argued to provide an effective limit of quantum gravity in almost-flat regime. Unfortunately, DSR is up to now plagued by many...

Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity (2005)

Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory (2005)

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...

Freidel, Laurent, Livine, Etera R.

We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as...

Entanglement of zero angular momentum mixtures and black hole entropy (2005)

Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators (2005)

We calculate the entanglement of formation and the entanglement of distillation for arbitrary mixtures of the zero spin states on an arbitrary-dimensional bipartite Hilbert space. Such states are...

Some Remarks on the Semi-Classical Limit of Quantum Gravity (2005)

Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how...

Some Remarks on the Semi-Classical Limit of Quantum Gravity (2005)

One of the most important issues in quantum gravity is to identify its semi-classical regime. First the issue is to define for we mean by a semi-classical theory of quantum gravity, then we would...

Etera R. Livine

One of the most important issues in quantum gravity is to identify its semi-classical regime. First the issue is to define for we mean by a semi-classical theory of quantum gravity, then we would...

Physics of Deformed Special Relativity (2004)

Physics of Deformed Special Relativity: Relativity Principle revisited (2004)

In many different ways, Deformed Special Relativity (DSR) has been argued to provide an effective limit of quantum gravity in almost-flat regime. Unfortunately DSR is up to now plagued by many...

Special Relativity as a non commutative geometry: Lessons for Deformed Special Relativity (2004)

In many different ways, Deformed Special Relativity (DSR) has been argued to provide an effective limit of quantum gravity in almost-flat regime. Some experiments will soon be able to test some low...

Deformed Special Relativity as an effective flat limit of quantum gravity (2004)

Deformed Special Relativity (DSR) is obtained by imposing a maximal energy to Special Relativity and deforming the Lorentz symmetry (more exactly the Poincar\'e symmetry) to accommodate this...

Girelli, Florian, Livine, Etera R., Oriti, Daniele

We argue that a (slightly) curved space-time probed with a finite resolution, equivalently a finite minimal length, is effectively described by a flat non-commutative space-time. More precisely, a...

About Lorentz invariance in a discrete quantum setting (2004)

Three-dimensional Quantum Supergravity and Supersymmetric Spin Foam Models (2003)

A common misconception is that Lorentz invariance is inconsistent with a discrete spacetime structure and a minimal length: under Lorentz contraction, a Planck length ruler would be seen as smaller...

Livine, Etera R., Oeckl, Robert

We show how super BF theory in any dimension can be quantized as a spin foam model, generalizing the situation for ordinary BF theory. This is a first step toward quantizing supergravity theories. We...

Holonomic quantum computation in the presence of decoherence (2003)

Fuentes-Guridi, Ivette, Girelli, Florian, Livine, Etera R.

We present a scheme to study non-abelian adiabatic holonomies for open Markovian systems. As an application of our framework, we analyze the robustness of holonomic quantum computation against...

Quantizing speeds with the cosmological constant (2003)

Boucles et Mousses de Spin en Gravite Quantique (2003)

Considering the Barrett-Crane spin foam model for quantum gravity with (positive) cosmological constant, we show that speeds must be quantized and we investigate the physical implications of this...

Three-dimensional Quantum Supergravity and Supersymmetric Spin Foam Models (2003)

I review the formalism of loop quantum gravity, in both its real and complex formulations, and spin foam theory which is its path integral counterpart. Spin networks for non-compact groups are...

Livine, Etera R., Oeckl, Robert

We show how super BF theory in any dimension can be quantized as a spin foam model, generalizing the situation for ordinary BF theory. This is a first step toward quantizing supergravity theories. We...

Causality in spin foam models for quantum gravity (2003)

Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity (2003)

We describe how the Barrett-Crane spin foam model defines transition amplitudes for quantum gravity states and how causality can be consistently implemented in it.

Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity (2003)

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...

Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity (2002)

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...

BRST quantization of Matrix Chern-Simons Theory (2002)

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...

Livine, Etera R., Smolin, Lee

The BRST quantization of matrix Chern-Simons theory is carried out, the symmetries of the theory are analysed and used to constrain the form of the effective action.

Implementing causality in the spin foam quantum geometry (2002)

SU(2) Loop Quantum Gravity seen from Covariant Theory (2002)

We analyse the classical and quantum geometry of the Barrett-Crane spin foam model for four dimensional quantum gravity, explaining why it has to be considering as a covariant realization of the...

Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity (2002)

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''...

Livine, Etera R

In the search for a covariant formulation for Loop Quantum Gravity, spin foams have arised as the corresponding discrete space-time structure and, among the different models, the Barrett-Crane model...

Spin Networks for Non-Compact Groups (2002)

Freidel, Laurent, Livine, Etera R.

Spin networks are natural generalization of Wilson loops functionals. They have been extensively studied in the case where the gauge group is compact and it has been shown that they naturally form a...

SU(2) Loop Quantum Gravity seen from Covariant Theory (2002)

SU(2) Loop Quantum Gravity seen from Covariant Theory (2002)

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\'\'...