相关论文: Geometric Structures and Loop Variables in (2+1)-D…

The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…

We perform the two loop level renormalization of quantum gravity in $2+\epsilon$ dimensions. We work in the background gauge whose manifest covariance enables us to use the short distance expansion of the Green's functions. We explicitly…

We study point particles in 2+1 dimensional first order gravity using a triangulation to fix the connection and frame-field. The Hamiltonian is reduced to a boundary term which yields the total mass. The triangulation is dynamical with…

We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.

We describe an approach to the quantization of (2+1)--dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q--commutation relation. Solutions of diagonal and…

In the context of the quest for a holographic formulation of quantum gravity, we investigate the basic boundary theory structure for loop quantum gravity. In 3+1 space-time dimensions, the boundary theory lives on the 2+1-dimensional…

We review some attempts of reformulating both gauge theory and general relativity in terms of holonomy-dependent loop variables. The emphasis lies on exhibiting the underlying mathematical structures, which often are not given due attention…

Finding diffeomorphism-invariant observables to characterize the properties of gravity and spacetime at the Planck scale is essential for making progress in quantum gravity. The holonomy and Wilson loop of the Levi-Civita connection are…

Two-dimensional Maxwell-dilaton quantum gravity, which covers a large family of the actions for two-dimensional gravity (in particular, string-inspired models) is investigated. Charged black holes which appear in the theory are briefly…

Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a…

The 4-dimensional metric $f(\R)$ theories of gravity are cast into connection-dynamical formalism with real $\SU(2)$-connections as configuration variables. Through this formalism, the classical metric $f(\R)$ theories are quantized by…

We investigate rotation and rotating structures in (2+1)-dimensional Einstein gravity. We show that rotation generally leads to pathological physical situations.

We investigate the $1+1+2$ covariant formalism in the presence of nonmetricity. Focusing on Locally Rotationally Symmetric spacetimes, we show how nonmetricity affects all the kinematic quantities involved in the covariant $1+1+2$…

We relate three-dimensional loop quantum gravity to the combinatorial quantisation formalism based on the Chern-Simons formulation for three-dimensional Lorentzian and Euclidean gravity with vanishing cosmological constant. We compare the…

In order to study 3d loop quantum gravity coupled to matter, we consider a simplified model of abelian quantum gravity, the so-called U(1)^3 model. Abelian gravity coupled to a scalar field shares a lot of commonalities with parameterized…

These lectures briefly review our current understanding of classical and quantum gravity in three spacetime dimensions, concentrating on the quantum mechanics of closed universes and the (2+1)-dimensional black hole. Three formulations of…

We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass…

General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…

The purpose of this review is to describe in some detail the mathematical relationship between geometrodynamics and connection dynamics in the context of the classical theories of 2+1 and 3+1 gravity. I analyze the standard Einstein-Hilbert…

We present a complete quantization of Lorentzian D=1+2 gravity with cosmological constant, coupled to a set of topological matter fields. The approach of Loop Quantum Gravity is used thanks to a partial gauge fixing leaving a residual gauge…