38 citations · 209 across the 12 of their papers we have counts for
11 papers · 1 filter
Canonical quantum gravity in the Vassiliev invariants arena: II. Constraints, habitats and consistency of the constraint algebra
Cayetano Di Bartolo, Rodolfo Gambini, Jorge Griego +1
In a companion paper we introduced a kinematical arena for the discussion of the constraints of canonical quantum gravity in the spin network representation based on Vassiliev inva…
Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure
Cayetano Di Bartolo, Rodolfo Gambini, Jorge Griego +1
We generalize the idea of Vassiliev invariants to the spin network context, with the aim of using these invariants as a kinematical arena for a canonical quantization of gravity. T…
Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants
C. Di Bartolo, R. Gambini, J. Griego +1
We present a quantization of the Hamiltonian and diffeomorphism constraint of canonical quantum gravity in the spin network representation. The novelty consists in considering a sp…
Vassiliev invariants: a new framework for quantum gravity
Rodolfo Gambini, Jorge Griego, Jorge Pullin
We show that Vassiliev invariants of knots, appropriately generalized to the spin network context, are loop differentiable in spite of being diffeomorphism invariant. This opens th…
Chern--Simons states in spin-network quantum gravity
Rodolfo Gambini, Jorge Griego, Jorge Pullin
In the context of canonical quantum gravity in terms of Ashtekar's new variables, it is known that there exists a state that is annihilated by all the quantum constraints and that…
Extended knots and the space of states of quantum gravity
Jorge Griego
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 a…
On the extended loop calculus
Jorge Griego
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 s…
The Kauffman bracket and the Jones polynomial in quantum gravity
Jorge Griego
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…
The space of states of quantum gravity in terms of loops and extended loops: some remarks
Cayetano Di Bartolo, Rodolfo Gambini, Jorge Griego +1
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…
Extended Loops: A New Arena for Nonperturbative Quantum Gravity
C. Di Bartolo, R. Gambini, J. Griego +1
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 extens…
The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space
Cayetano Di Bartolo, Rodolfo Gambini, Jorge Griego
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 diffeomorphis…