Related papers: Point particles in 2+1 dimensions: general relativ…
We embark on the vast program of integrating the dynamics of Loop Quantum Gravity (LQG). Adopting the strategy of decomposing spin network states into small blocks of (quantum) geometry which can later be glued back together, we focus on…
We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume…
We show that General Relativity can be formulated as a constrained topological theory for flat 2-connections associated to the Poincar\'e 2-group. Matter can be consistently coupled to gravity in this formulation. We also show that the edge…
We study the loop representation of the quantum theory for 2+1 dimensional general relativity on a manifold, $M = {\cal T}^2 \times {\cal R}$, where ${\cal T}^2$ is the torus, and compare it with the connection representation for this…
We consider the theory of pure gravity in 2+1 dimensions, with negative cosmological constant. The theory contains simple matter in the form of point particles; the later are classically described as lines of conical singularities. We…
The coupling of gravity to matter is explored in the linearized gravity limit. The usual derivation of gravity-matter couplings within the quantum-field-theoretic framework is reviewed. A number of inconsistencies between this derivation of…
We formulate quantum gravity in $2+\epsilon$ dimensions in such a way that the conformal mode is explicitly separated. The dynamics of the conformal mode is understood in terms of the oversubtraction due to the one loop counter term. The…
We present the exact solution of two-body motion in (1+1) dimensional dilaton gravity by solving the constraint equations in the canonical formalism. The determining equation of the Hamiltonian is derived in a transcendental form and the…
We revisit pure quantum cosmology in three dimensions. The Wheeler-DeWitt equation can be solved perturbatively and the dynamics reduces to a particle on moduli space. Its time evolution is equivalent to the $T\overline{T}$ deformation.…
Content: 1. Introduction 2. Regge calculus and dynamical triangulations Simplicial manifolds and piecewise linear spaces - dual complex and volume elements - curvature and Regge action - topological invariants - quantum Regge calculus -…
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted…
We introduce a model designed to describe charged particles as stable topological solitons of a field with values on the internal space S^3. These solitons behave like particles with relativistic properties like Lorentz contraction and…
We provide a general algorithm to construct a Hamiltonian, such that its dynamical flow covariantly defines any given spherically symmetric and static metric. This Hamiltonian is defined as a linear combination of the standard (general…
In this paper we derive an expression for the conserved Pauli-Lubanski scalar in 't Hooft's polygon approach to 2+1-dimensional gravity coupled to point particles. We find that it is represented by an extra spatial shift $\Delta$ in…
A new path equation in absolute parallelism (AP) geometry is derived. The equation is a generalization of three path equations derived in a previous work. It can be considered as a geodesic equation modified by a torsion term, whose…
We discuss scaling relations in four dimensional simplicial quantum gravity. Using numerical results obtained with a new algorithm called ``baby universe surgery'' we study the critical region of the theory. The position of the phase…
We consider the quantization of space-times which can possess different topologies within a symmetry reduced version of Wheeler-DeWitt theory. The quantum states are defined from a natural decomposition as an outer-product of a topological…
The construction of effective Hamiltonians describing corrections to flat space particle dynamics arising from the granularity of space at very short distances is discussed in the framework of an heuristic approach to the semiclassical…
An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt…
Motivated by recent developments in the theory of gravitation, we revisit the idea of topological variations, originally introduced by Wheeler and Hawking, from a rigorous perspective. Starting from a localized version of the…