The Fine Structure of SU(2) Intertwiners from U(N) Representations (2009)
Freidel, Laurent, Livine, Etera R.
In this work we study the Hilbert space space of N-valent SU(2) intertwiners with fixed total spin, which can be identified, at the classical level, with a space of convex polyhedra with N face and...
Group field theory renormalization - the 3d case: power counting of divergences (2009)
Freidel, Laurent, Gurau, Razvan, Oriti, Daniele
We take the first steps in a systematic study of Group Field Theory renormalization, focusing on the Boulatov model for 3D quantum gravity. We define an algorithm for constructing the 2D...
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...
Inner brane: A D3-brane in the Nappi-Witten model from an inner group automorphism (2009)
Cheung, Yeuk-Kwan E., Freidel, Laurent
WZW models are abstract conformal field theories with an infinite dimensional symmetry which accounts for their integrability, and at the same time they have a sigma model description of closed...
Quantum geometry from phase space reduction (2009)
Conrady, Florian, Freidel, Laurent
In this work we give an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra. The main outcome is a formula that describes...
Infinite-Dimensional Representations of 2-Groups (2008)
Baez, John C., Baratin, Aristide, Freidel, Laurent, Wise, Derek K.
A "2-group" is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, 2-groups have representations on "2-vector...
Modified gravity without new degrees of freedom (2008)
We show that the new type of "non-metric" gravity theories introduced independently by Bengtsson and Krasnov can in fact be reexpressed explicitely as a metrical theory coupled to an auxiliary field....
On the semiclassical limit of 4d spin foam models (2008)
Conrady, Florian, Freidel, Laurent
We study the semiclassical properties of the Riemannian spin foam models with Immirzi parameter that are constructed via coherent states. We show that in the semiclassical limit the quantum spin foam...
Path integral representation of spin foam models of 4d gravity (2008)
Conrady, Florian, Freidel, Laurent
We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of...
In this note we clarify the dictionary between pure quantum gravity on the bulk in the presence of a cosmological constant and a CFT on the boundary. We show for instance that there is a general...
On the spectrum of pure Yang-Mills theory (2008)
Freidel, Laurent, Leigh, Robert G., Minic, Djordje, Yelnikov, Alexandr
In this note we discuss the wave functional approach to the spectrum of pure Yang-Mills theory in 2+1 and 3+1 dimensions by highlighting the issues of dynamical mass generation and the role played by...
$\kappa$-Minkowski space, scalar field, and the issue of Lorentz invariance (2007)
Freidel, Laurent, Kowalski-Glikman, Jerzy
We describe $\kappa$-Minkowski space and its relation to group theory. The group theoretical picture makes it possible to analyze the symmetries of this space. As an application of this analysis we...
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...
A New Spin Foam Model for 4d Gravity (2007)
Freidel, Laurent, Krasnov, Kirill
Starting from Plebanski formulation of gravity as a constrained BF theory we propose a new spin foam model for 4d Riemannian quantum gravity that generalises the well-known Barrett-Crane model and...
Linearized dynamics from the 4-simplex Regge action (2007)
Dittrich, Bianca, Freidel, Laurent, Speziale, Simone
We study the relation between the hessian matrix of the riemannian Reggae action on a 4-simplex and linearized quantum gravity. We give an explicit formula for the hessian as a function of the...
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...
From noncommutative kappa-Minkowski to Minkowski space-time (2006)
Freidel, Laurent, Kowalski-Glikman, Jerzy, Nowak, Sebastian
We show that free $\kappa$-Minkowski space field theory is equivalent to a relativistically invariant, non local, free field theory on Minkowski space-time. The field theory we obtain has in spectrum...
Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams (2006)
Baratin, Aristide, Freidel, Laurent
We show how Feynman amplitudes of standard QFT on flat and homogeneous space can naturally be recast as the evaluation of observables for a specific spin foam model, which provides dynamics for the...
Towards a solution of pure Yang-Mills theory in 3+1 dimensions (2006)
Freidel, Laurent, Leigh, Robert G., Minic, Djordje
We discuss an analytic approach towards the solution of pure Yang-Mills theory in 3+1 dimensional spacetime. The approach is based on the use of local gauge invariant variables in the Schr\"odinger...
In this work we discuss an analytic approach towards the solution of pure Yang-Mills theory in 3+1 dimensional spacetime which strongly suggests that the recent strategy already applied to pure...
Hidden Quantum Gravity in 3d Feynman diagrams (2006)
Baratin, Aristide, Freidel, Laurent
In this work we show that 3d Feynman amplitudes of standard QFT in flat and homogeneous space can be naturally expressed as expectation values of a specific topological spin foam model. The main...
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...
Quantum Gravity, Torsion, Parity Violation and all that (2005)
Freidel, Laurent, Minic, Djordje, Takeuchi, Tatsu
We discuss the issue of parity violation in quantum gravity. In particular, we study the coupling of fermionic degrees of freedom in the presence of torsion and the physical meaning of the Immirzi...
A group field theory for 3d quantum gravity coupled to a scalar field (2005)
Freidel, Laurent, Oriti, Daniele, Ryan, James
We present a new group field theory model, generalising the Boulatov model, which incorporates both 3-dimensional gravity and matter coupled to gravity. We show that the Feynman diagram amplitudes of...
Group Field Theory: An overview (2005)
We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so...
Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity (2005)
Freidel, Laurent, Livine, Etera R., Rovelli, Carlo
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...
Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory (2005)
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...
Quantum gravity in terms of topological observables (2005)
Freidel, Laurent, Starodubtsev, Artem
We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes...
Freidel, Laurent, Mann, R. B., Popescu, Eugeniu M.
We consider a topological field theory derived from the Chern - Simons action in (2+1) dimensions with the I(ISO(2,1)) group,and we investigate in detail the canonical structure of this...
Ponzano-Regge model revisited II: Equivalence with Chern-Simons (2004)
Freidel, Laurent, Louapre, David
We provide a mathematical definition of the gauge fixed Ponzano-Regge model showing that it gives a measure on the space of flat connections whose volume is well defined. We then show that the...
Strings in gravimagnetic fields (2004)
Cheung, Yeuk-Kwan E., Freidel, Laurent, Savvidy, Konstantin
We provide a complete solution of closed strings propagating in Nappi-Witten space. Based on the analysis of geodesics we construct the coherent wavefunctions which approximate as closely as possible...
Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles (2004)
Freidel, Laurent, Louapre, David
We show how to properly gauge fix all the symmetries of the Ponzano-Regge model for 3D quantum gravity. This amounts to do explicit finite computations for transition amplitudes. We give the...
The linearization of the Kodama state (2003)
We study the question of whether the linearization of the Kodama state around classical deSitter spacetime is normalizable in the inner product of the theory of linearized gravitons on deSitter...
Strings in Gravimagnetic Fields (2003)
Cheung, Yeuk-Kwan E., Freidel, Laurent, Savvidy, Konstantin
We provide a complete solution of closed strings propagating in Nappi-Witten space. Based on the analysis of geodesics we construct the coherent wavefunctions which approximate as closely as possible...
2+1 gravity and Doubly Special Relativity (2003)
Freidel, Laurent, Kowalski-Glikman, Jerzy, Smolin, Lee
It is shown that gravity in 2+1 dimensions coupled to point particles provides a nontrivial example of Doubly Special Relativity (DSR). This result is obtained by interpretation of previous results...
Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity (2003)
Freidel, Laurent, Livine, Etera R., Rovelli, Carlo
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 (2003)
Freidel, Laurent, Livine, Etera R., Rovelli, Carlo
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)
Freidel, Laurent, Livine, Etera R., Rovelli, Carlo
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...
Diffeomorphisms and spin foam models (2002)
Freidel, Laurent, Louapre, David
We study the action of diffeomorphisms on spin foam models. We prove that in 3 dimensions, there is a residual action of the diffeomorphisms that explains the naive divergences of state sum models....
Non-perturbative summation over 3D discrete topologies (2002)
Freidel, Laurent, Louapre, David
We construct a group field theory which realizes the sum of gravity amplitudes over all three dimensional topologies trough a perturbative expansion. We prove this theory to be uniquely Borel...
Asymptotics of 6j and 10j symbols (2002)
Freidel, Laurent, Louapre, David
It is well known that the building blocks for state sum models of quantum gravity are given by 6j and 10j symbols. In this work we study the asymptotics of these symbols by using their expressions as...
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...
2D Conformal Field Theories and Holography (2002)
Freidel, Laurent, Krasnov, Kirill
It is known that the chiral part of any 2d conformal field theory defines a 3d topological quantum field theory: quantum states of this TQFT are the CFT conformal blocks. The main aim of this paper...
The Fuzzy Sphere Star-Product and Spin Networks (2001)
Freidel, Laurent, Krasnov, Kirill
We analyze the expansion of the fuzzy sphere non-commutative product in powers of the non-commutativity parameter. To analyze this expansion we develop a graphical technique that uses spin networks....
A Ponzano-Regge model of Lorentzian 3-Dimensional gravity (2001)
We present the construction of the partition function of 3-dimensional gravity in the Lorentzian regime as a state sum model over a triangulation. This generalize the work of Ponzano and Regge to the...
Simple Spin Networks as Feynman Graphs (1999)
Freidel, Laurent, Krasnov, Kirill
We show how spin networks can be described and evaluated as Feynman integrals over an internal space. This description can, in particular, be applied to the so-called simple SO(D) spin networks that...
Spin Foam Models and the Classical Action Principle (1998)
Freidel, Laurent, Krasnov, Kirill
We propose a new systematic approach that allows one to derive the spin foam (state sum) model of a theory starting from the corresponding classical action functional. It can be applied to any theory...
Discrete Space-Time Volume for 3-Dimensional BF Theory and Quantum Gravity (1998)
Freidel, Laurent, Krasnov, Kirill
The Turaev-Viro state sum invariant is known to give the transition amplitude for the three dimensional BF theory with cosmological term, and its deformation parameter hbar is related with the...
From sl(2) Kirby weight systems to the asymptotic 3-manifold invariant (1998)
We give a construction of Kirby weight systems associated to sl(2) and valued into the finite field Z/pZ. We show that it is possible to apply this sequence of weight systems on the universal...
Vassiliev knot invariants and Chern-Simons perturbation theory to all orders (1996)
Altschuler, Daniel, Freidel, Laurent
At any order, the perturbative expansion of the expectation values of Wilson lines in Chern-Simons theory gives certain integral expressions. We show that they all lead to knot invariants. Moreover...
On Universal Vassiliev Invariants (1994)
Altschuler, Daniel, Freidel, Laurent
Using properties of ordered exponentials and the definition of the Drinfeld associator as a monodromy operator for the Knizhnik-Zamolodchikov equations, we prove that the analytic and the...
Freidel, Laurent, Maillet, J. M.
Using a geometrical approach to the quantum Yang-Baxter equation, the quantum algebra ${\cal U}_{\hbar}(sl_{2})$ and its universal quantum $R$-matrix are explicitely constructed as functionals of the...