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The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional surfaces. The space of states of the theory is the direct sum of the spaces of invariant tensors of a quantum group Gq over allâ€¦ (More)

A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal sets, which consist of spin networks representing quantum states of the gravitational field joined together by labeledâ€¦ (More)

Quantum causal histories are defined to be causal sets with Hilbert spaces attached to each event and local unitary evolution operators. The reflexivity, antisymmetry, and transitivity properties of a causal set are preserved in the quantum history as conditions on the evolution operators. A quantum causal history in which transitivity holds can be treatedâ€¦ (More)

We illustrate the relationship between spin networks and their dual representation by labelled triangulations of space in 2+1 and 3+1 dimensions. We apply this to the recent proposal for causal evolution of spin networks. The result is labelled spatial triangulations evolving with transition amplitudes given by labelled spacetime simplices. The formalism isâ€¦ (More)

- Sundance O. Bilson-Thompson, Fotini Markopoulou, L. N. Smolin
- 2006

We show that a class of background independent models of quantum spacetime have local excitations that can be mapped to the first generation fermions of the standard model of particle physics. These states propagate coherently as they can be shown to be noiseless subsystems of the microscopic quantum dynamics[2]. These are identified in terms of certainâ€¦ (More)

We formulate the problem of finding the low-energy limit of spin foam models as a coarse-graining problem in the sense of statistical physics. This suggests that renormalization group methods may be used to find that limit. However, since spin foams are models of spacetime at Planck scale, novel issues arise: these microscopic models are sums overâ€¦ (More)

We provide a precise definition and analysis of quantum causal histories (QCHâ€™s). A QCH consists of a discrete, locally finite, causal pre-spacetime with matrix algebras encoding the quantum structure at each event. The evolution of quantum states and observables is described by completely positive maps between the algebras at causally related events. Weâ€¦ (More)

A review is given of recent work aimed at constructing a quantum theory of cosmology in which all observables refer to information measurable by observers inside the universe. At the classical level the algebra of observables should be modified to take into account the fact that observers can only give truth values to observables that have to do with theirâ€¦ (More)

Quantum graphity is a background-independent model for emergent macroscopic locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly connected and the physics is invariant under the full symmetric group acting on the vertices. We present evidenceâ€¦ (More)

We propose that Kreimerâ€™s method of Feynman diagram renormalization via a Hopf algebra of rooted trees can be fruitfully employed in the analysis of block spin renormalization or coarse graining of inhomogeneous statistical systems. Examples of such systems include spin foam formulations of non-perturbative quantum gravity as well as lattice gauge and spinâ€¦ (More)