Related papers: The Extended Loop Representation of Quantum Gravit…
We propose a new representation for gauge theories and quantum gravity. It can be viewed as a generalization of the loop representation. We make use of a recently introduced extension of the group of loops into a Lie Group. This extension…
In the loop representation the quantum constraints of gravity can be solved. This fact allowed significant progress in the understanding of the space of states of the theory. The analysis of the constraints over loop dependent wavefunctions…
A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of…
The Gauss constraint in the extended loop representation for quantum gravity is studied. It is shown that there exists a sector of the state space that is rigorously gauge invariant without the generic convergence issues of the extended…
We review the application of the loop representation to gauge theories and general relativity. The emphasis lies on exhibiting the loop calculus techniques, and their application to the canonical quantization. We discuss the role that knot…
This article reviews the status of several solutions to all the constraints of quantum gravity that have been proposed in terms of loops and extended loops. We discuss pitfalls of several of the results and in particular discuss the issues…
New results from the new variables/loop representation program of nonperturbative quantum gravity are presented, with a focus on results of Ashtekar, Rovelli and the author which greatly clarify the physical interpretation of the quantum…
Since the gauge group underlying 2+1-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately…
In a remarkable paper, T. Koslowski introduced kinematical representations for loop quantum gravity in which there is a non-degenerate spatial background metric present. He also considered their properties, and showed that Gauss and…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
An analysis of the action of the Hamiltonian constraint of quantum gravity on the Kauffman bracket and Jones knot polynomials is proposed. It is explicitely shown that the Kauffman bracket is a formal solution of the Hamiltonian constraint…
We present a generalization of the first-order formalism used to describe the dynamics of a classical system. The generalization is then applied to the first-order action that describes General Relativity. As a result we obtain equations…
Some features of extended loops are considered. In particular, the behaviour under diffeomorphism transformations of the wavefunctions with support on the extended loop space are studied. The basis of a method to obtain analytical…
We construct the regularised Wheeler-De Witt operator demanding that the algebra of constraints of quantum gravity is anomaly free. We find that for a subset of all wavefunctions being integrals of scalar densities this condition can be…
This series of lectures gives a simple and self-contained introduction to the non-perturbative and background independent loop approach of canonical quantum gravity. The Hilbert space of kinematical quantum states is constructed and a…
Vielbeins are necessary when coupling General Relativity (GR) to fermionic matter. This enhances the gauge group of GR to include local Lorentz transformations. In view of a reduced phase space formulation of quantum gravity, in this work…
A new representation for canonical gravity and supergravity is presented, which combines advantages of Ashtekar's and the Wheeler~DeWitt representation: it has a nice geometric structure and the singular metric problem is absent. A formal…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…
We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing and introducing loops, we proceed backwards, setting up constraints in the…