arXiv subjects

Karim Noui

Publications and source records attributed to Karim Noui.

81 records · Page 5Linked to original sources

arXiv2006

Three Dimensional Loop Quantum Gravity: Particles and the Quantum Double

It is well known that the quantum double structure plays an important role in three dimensional quantum gravity coupled to matter field. In this paper, we show how this algebraic structure emerges in the context of three dimensional Riemannian loop quantum gravity (LQG) coupled to a finite number of massive spinless point particles. In LQG, physical states are usually constructed from the notion of SU(2) cylindrical functions on a Riemann surface $Σ$ and the Hilbert structure is defined by the Ashtekar-Lewandowski measure. In the case where $Σ$ is the sphere $S^2$, we show that the physical Hilbert space is in fact isomorphic to a tensor product of simple unitary representations of the Drinfeld double DSU(2): the masses of the particles label the simple representations, the physical states are tensor products of vectors of simple representations and the physical scalar product is given by intertwining coefficients between simple representations. This result is generalized to the case of any Riemann surface $Σ$.

gr-qc↗

arXiv2006

Three dimensional Loop Quantum Gravity: towards a self-gravitating Quantum Field Theory

In a companion paper, we have emphasized the role of the Drinfeld double DSU(2) in the context of three dimensional Riemannian Loop Quantum Gravity coupled to massive spinless point particles. We make use of this result to propose a model for a self-gravitating quantum field theory (massive spinless non-causal scalar field) in three dimensional Riemannian space. We start by constructing the Fock space of the free self-gravitating field: the vacuum is the unique DSU(2) invariant state, one-particle states correspond to DSU(2) unitary irreducible simple representations and any multi-particles states is obtained as the symmetrized tensor product between simple representations. The associated quantum field is defined by the usual requirement of covariance under DSU(2). Then, we introduce a DSU(2)-invariant self-interacting potential (the obtained model is a Group Field Theory) and compute explicitely the lowest order terms (in the self-interaction coupling constant $λ$) of the propagator and of the three-points function. Finally, we compute the lowest order quantum gravity corrections (in the Newton constant G) to the propagator and to the three-points function.

gr-qc↗

arXiv2005

Three dimensional loop quantum gravity: physical scalar product and spin foam models

In this paper, we address the problem of the dynamics in three dimensional loop quantum gravity with zero cosmological constant. We construct a rigorous definition of Rovelli's generalized projection operator from the kinematical Hilbert space--corresponding to the quantization of the infinite dimensional kinematical configuration space of the theory--to the physical Hilbert space. In particular, we provide the definition of the physical scalar product which can be represented in terms of a sum over (finite) spin-foam amplitudes. Therefore, we establish a clear-cut connection between the canonical quantization of three dimensional gravity and spin-foam models. We emphasize two main properties of the result: first that no cut-off in the kinematical degrees of freedom of the theory is introduced (in contrast to standard `lattice' methods), and second that no ill-defined sum over spins (`bubble' divergences) are present in the spin foam representation.

gr-qc↗

arXiv2004

On the Physical Hilbert Space of Loop Quantum Cosmology

In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a cosmological constant, the model is exactly solvable and we show explicitly that the physical Hilbert space is separable consisting of a single physical state. We extend the model to the Lorentzian sector and discuss important implications for standard loop quantum cosmology.

gr-qc↗

arXiv2004

Background independence in a nutshell

We study how physical information can be extracted from a background independent quantum system. We use an extremely simple `minimalist' system that models a finite region of 3d euclidean quantum spacetime with a single equilateral tetrahedron. We show that the physical information can be expressed as a boundary amplitude. We illustrate how the notions of "evolution" in a boundary proper-time and "vacuum" can be extracted from the background independent dynamics.

gr-qc↗

arXiv2004

Three dimensional loop quantum gravity: coupling to point particles

We consider the coupling between three dimensional gravity with zero cosmological constant and massive spinning point particles. First, we study the classical canonical analysis of the coupled system. Then, we go to the Hamiltonian quantization generalizing loop quantum gravity techniques. We give a complete description of the kinematical Hilbert space of the coupled system. Finally, we define the physical Hilbert space of the system of self-gravitating massive spinning point particles using Rovelli's generalized projection operator which can be represented as a sum over spin foam amplitudes. In addition we provide an explicit expression of the (physical) distance operator between two particles which is defined as a Dirac observable.

gr-qc↗

arXiv2004

Observability and Geometry in Three dimensional quantum gravity

We consider the coupling between massive and spinning particles and three dimensional gravity. This allows us to construct geometric operators (distances between particles) as Dirac observables. We quantize the system a la loop quantum gravity: we give a description of the kinematical Hilbert space and construct the associated spin-foam model. We construct the physical disctance operator and consider its quantization.

gr-qc↗

arXiv2004

Dynamics of loop quantum gravity and spin foam models in three dimensions

We present a rigorous regularization of Rovellis's generalized projection operator in canonical 2+1 gravity. This work establishes a clear-cut connection between loop quantum gravity and the spin foam approach in this simplified setting. The point of view adopted here provides a new perspective to tackle the problem of dynamics in the physically relevant 3+1 case.

gr-qc↗

arXiv2002

Cosmological Deformation of Lorentzian Spin Foam Models

We study the quantum deformation of the Barrett-Crane Lorentzian spin foam model which is conjectured to be the discretization of Lorentzian Plebanski model with positive cosmological constant and includes therefore as a particular sector quantum gravity in de-Sitter space. This spin foam model is constructed using harmonic analysis on the quantum Lorentz group. The evaluation of simple spin networks are shown to be non commutative integrals over the quantum hyperboloid defined as a pile of fuzzy spheres. We show that the introduction of the cosmological constant removes all the infrared divergences: for any fixed triangulation, the integration over the area variables is finite for a large class of normalization of the amplitude of the edges and of the faces.

gr-qc↗