The evolution operator for states of gauge theories in the graph representation (closely related to the loop representation) is formulated as a weighted sum over worldsheets interpolating between… (More)

An action for simplicial euclidean general relativity involving only left-handed fields is presented. The simplicial theory is shown to converge to continuum general relativity in the Plebanski… (More)

The spin foam formalism [1–7] is a beautiful convergence of different approaches to general relativistic –or background independent– quantum field theory, and in particular to quantum gravity. A… (More)

We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry in proper time. We… (More)

Ashtekar’s canonical theory of classical complex Euclidean GR (no Lorentzian reality conditions) is found to be invariant under the full algebra of infinitesimal 4-diffeomorphisms, but non-invariant… (More)

Spin foam models are the path integral counterparts to loop quantized canonical theories. In the last few years several spin foam models of gravity have been proposed, most of which live on finite… (More)

A classical continuum theory corresponding to Barrett and Crane’s model of Euclidean quantum gravity is presented. The fields in this classical theory are those of SO(4) BF theory, a simple… (More)

In this paper, we discuss a covariant formulation of canonical quantum mechanics. This formulation is based on the propagator and on a representation of quantum states which we will call… (More)

Barrett and Crane have proposed a model of simplicial Euclidean quantum gravity in which a central role is played by a class of Spin(4) spin networks called “relativistic spin networks” which satisfy… (More)

A lattice model for four dimensional Euclidean quantum general relativity is proposed for a simplicial spacetime. It is shown how this model can be expressed in terms of a sum over worldsheets of… (More)