Related papers: An illustration of 2+1 gravity loop transform trou…
Non-abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher dimensional (2-dimensional in the present context) connection forms, and as such, it has been successfully applied to the…
In the context of quantum gravity for spacetimes of dimension 2+1, we describe progress in the construction of a quantum Goldman bracket for intersecting loops on surfaces. Using piecewise linear paths in R^2 (representing loops on the…
From the point of view of an uncompromising field theorist quantum gravity is beset with serious technical and, above all, conceptual problems with regard especially to the meaning of genuine "physical" observables. This situation is not…
The reduction of the dreibein formalism of 2+1 General Relativity to the holonomies is explicitly performed. We also show explicitly how to relate these holonomies to a geometry classically, and how to generate these holonomies from any…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
We discuss the structure of one-loop counterterms for the two-dimensional theory of gravitation in the covariant scheme and study the effect of quantum reparametrizations. Some of them are shown to be equivalent to the introduction of…
In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum…
We review uniqueness results for the kinematical part of loop quantum gravity. After sketching the general loop formalism, the holonomy-flux and the Weyl algebras are introduced. In both cases, then, diffeomorphism invariant representations…
A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general…
Dynamical black-hole scenarios have been developed in loop quantum gravity in various ways, combining results from mini and midisuperspace models. In the past, the underlying geometry of space-time has often been expressed in terms of line…
Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…
The recently proposed loop representation, used previously to find exact solutions to the quantum constraints of general relativity, is here used to quantize linearized general relativity. The Fock space of graviton states and its…
It is possible to implement a certain form of modified gravity inspired by loop quantization through non-bijective canonical transformations. The canonical nature might suggest that such modifications are guaranteed to preserve general…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
Covariant models of loop quantum gravity generically imply dynamical signature change at high density. This article presents detailed derivations that show the fruitful interplay of this new kind of signature change with wave-function…
Fundamental quantum gravity theories are known to be notoriously difficult to extract viable testable predictions out of. In this paper, we aim to incorporate putative quantum corrections coming from loop quantum gravity in deriving…
The weak coupling loop quantum theory with Abelian gauge group provides us a new perspective to study the weak coupling properties of LQG. In this paper, the weak coupling theory of all dimensional loop quantum gravity is established based…
The loop quantum gravity technique is applied to the free bosonic string. A Hilbert space similar to loop space in loop quantum gravity as well as representations of diffeomorphism and hamiltonian constraints on it are constructed. The…
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…