Three principles for canonical quantum gravity

We outline three principles that should guide us in the construction of a theory of canonical quantum gravity: 1) diffeomorphism invariance, 2) implementing the proper dynamics and related constraint algebra, 3) local Lorentz invariance. We illustrate each of them with its role in model calculations in loop quantum gravity

Canonical quantum gravity and consistent discretizations

This is a summary of the talk presented by JP at ICGC2004. It covered some developments in canonical quantum gravity occurred since ICGC2000, emphasizing the recently introduced consistent discretizations of general relativity.Comment: 8 pages, to appear in Praman

The general solution of the quantum Einstein equations?

We suggest how to interpret the action of the quantum Hamiltonian constraint of general relativity in the loop representation as a skein relation on the space of knots. Therefore, by considering knot polynomials that are compatible with that skein relation, one guarantees that all the quantum Einstein equations are solved. We give a particular example of such invariant and discuss the consistency of the constraint algebra in this approach.Comment: 3 pages, Revtex, 7 figures included with psfi

The Montevideo Interpretation of Quantum Mechanics: a short review

The Montevideo interpretation of quantum mechanics, which consists in supplementing environmental decoherence with fundamental limitations in measurement stemming from gravity, has been described in several publications. However, some of them appeared before the full picture provided by the interpretation was developed. As such it can be difficult to get a good understanding via the published literature. Here we summarize it in a self contained brief presentation including all its principal elements.Comment: 10 pages, RevTex, version published in special issue of Entrop

Gravitation in terms of observables

In the 1960's, Mandelstam proposed a new approach to gauge theories and gravity based on loops. The program for gauge theories was completed for Yang--Mills theories by Gambini and Trias in the 1980's. Gauge theories could be understood as representations of certain group: the group of loops. The same formalism could not be implemented at that time for the gravitational case. Here we would like to propose an extension to the case of gravity. The resulting theory is described in terms of loops and open paths and can provide the underpinning for a new quantum representation for gravity distinct from the one used in loop quantum gravity or string theory. In it, space-time points are emergent entities that would only have quasi-classical status. The formulation may be given entirely in terms of Dirac observables that form a complete set of gauge invariant functions that completely define the Riemannian geometry of the spacetime. At the quantum level this formulation will lead to a reduced phase space quantization free of any constraints.Comment: 39 pages, 15 figures, RevTex, version published in CQ

Variational derivation of exact skein relations from Chern--Simons theories

The expectation value of a Wilson loop in a Chern--Simons theory is a knot invariant. Its skein relations have been derived in a variety of ways, including variational methods in which small deformations of the loop are made and the changes evaluated. The latter method only allowed to obtain approximate expressions for the skein relations. We present a generalization of this idea that allows to compute the exact form of the skein relations. Moreover, it requires to generalize the resulting knot invariants to intersecting knots and links in a manner consistent with the Mandelstam identities satisfied by the Wilson loops. This allows for the first time to derive the full expression for knot invariants that are suitable candidates for quantum states of gravity (and supergravity) in the loop representation. The new approach leads to several new insights in intersecting knot theory, in particular the role of non-planar intersections and intersections with kinks.Comment: 16 pages, RevTeX, 15 figures include

Lorentz violations in canonical quantum gravity

This is a summary of a talk given at the CP01 meeting on possible Lorentz anomalies in canonical quantum gravity. It briefly reviews some initial explorations on the subject that have taken place recently, and should be only be seen as a short pointer to the literature on the subject, mostly for outsiders.Comment: 4 pages, Revtex. Talk given at CP01. To appear in proceeding