Related papers: Extended Loops: A New Arena for Nonperturbative Qu…
A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum…
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…
We introduce a new basis on the state space of non-perturbative quantum gravity. The states of this basis are linearly independent, are well defined in both the loop representation and the connection representation, and are labeled by a…
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…
It has been pointed out that the holonomy of generic extended loops is not gauge covariant. We show how to define a family of extended loops for which previous criticism does not apply. We also give sufficient conditions that extended loops…
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…
Solutions to both the diffeomorphism and the hamiltonian constraint of quantum gravity have been found in the loop representation, which is based on Ashtekar's new variables. While the diffeomorphism constraint is easily solved by…
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…
We propose a naive unification of Electromagnetism and General Relativity based on enlarging the gauge group of Ashtekar's new variables. We construct the connection and loop representations and analyze the space of states. In the loop…
We introduce a new loop expansion that provides a resolution of the identity in the Hilbert space of loop quantum gravity on a fixed graph. We work in the bosonic representation obtained by the canonical quantization of the spinorial…
Some time ago it was conjectured that the coefficients of an expansion of the Jones polynomial in terms of the cosmological constant could provide an infinite string of knot invariants that are solutions of the vacuum Hamiltonian constraint…
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…
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…
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 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 existing approaches to quantization of gravity aim at giving quantum description of 3-geometry following to the ideas of the Wheeler -- DeWitt geometrodynamics. In this description the role of gauge gravitational degrees of freedom is…
A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously…