Proposals that quantum gravity gives rise to non-commutative spacetime geometry and deformations of Poincaré symmetry are examined in the context of (2+1)dimensional quantum gravity. The results are expressed in five lessons, which summarise how the gravitational constant, Planck’s constant and the cosmological constant enter the non-commutative and non-cocommutative structures arising in (2+1)...

After motivating why the study of asymptotically flat spaces is important in loop quantum gravity, we review the extension of the standard framework of this theory to the asymptotically flat sector detailed in [1]. In particular, we provide a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. States in these Hilbert spaces can be int...

The application of quantum theory to gravity is beset with many technical and conceptual problems. After a short tour d’horizon of recent attempts to master those problems by the introduction of new approaches, we show that the aim, a background independent quantum theory of gravity, can be reached in a particular area, 2d dilaton quantum gravity, without any assumptions beyond standard quantum...

This is an introduction to spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity, topological quantum field theories, path integral quantum gravity, lattice field theory, matrix models, category theory, statistical mechanics. We describe the general formalism and ideas of spin foa...

I briefly review the current status of quantum gravity. After giving some general motivations for the need of such a theory, I discuss the main approaches in quantizing general relativity: Covariant approaches (perturbation theory, effective theory, and path integrals) and canonical approaches (quantum geometrodynamics, loop quantum gravity). I then address quantum gravitational aspects of stri...

No theory of four-dimensional quantum gravity exists as yet. In this situation the two-dimensional theory, which can be analyzed by conventional field-theoretical methods, can serve as a toy model for studying some aspects of quantum gravity. It represents one of the rare settings in a quantum-gravitational context where one can calculate quantities truly independent of any background geometry....

Four-dimensional (4D) simplicial quantum gravity coupled to both scalar fields (NX) and gauge fields (NA) has been studied using Monte-Carlo simulations. The matter dependence of the string susceptibility exponent γ (4) is estimated. Furthermore, we compare our numerical results with Background-Metric-Independent (BMI) formulation conjectured to describe the quantum field theory of gravity in 4...

A sketch of the affine quantum gravity program illustrates a different perspective on several difficult issues of principle: metric positivity; quantum anomalies; and nonrenormalizability. Quantum gravity is under study from several viewpoints. Brane world scenarios and loop quantum gravity represent the two most popular approaches [1], yet alternative viewpoints may also deserve consideration....

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 projector operator onto physical quantum gravity states. We discuss how causality requirements can be consistently implemented in this framework, and construct causal transiton amplitudes between quantu...

This work is a combinatorial study of quantum gravity models related to Lorentzian quantum gravity. These models are discrete combinatorial objects called dynamical triangulations. They are related to classical combinatorial objects: Dyck paths, heaps, . . . This work is in collaboration with Xavier Viennot and is part of the speaker’s thesis [4]. Quantum gravity is a quantum description of the...