211 research outputs found
Locality and Translations in Braided Ribbon Networks
An overview of microlocality in braided ribbon networks is presented.
Following this, a series of definitions are presented to explore the concept of
microlocality and the topology of ribbon networks. Isolated substructure of
ribbon networks are introduced, and a theorem is proven that allows them to be
relocated. This is followed by a demonstration of microlocal translations.
Additionally, an investigation into macrolocality and the implications of
invariants in braided ribbon networks are presented.Comment: 12 pages, 12 figure
Quantum causal histories
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 treated as ``directed'' topological
quantum field theory. Two examples of such histories are described.Comment: 16 pages, epsfig latex. Some clarifications, minor corrections and
references added. Version to appear in Classical and Quantum Gravit
Disordered locality in loop quantum gravity states
We show that loop quantum gravity suffers from a potential problem with
non-locality, coming from a mismatch between micro-locality, as defined by the
combinatorial structures of their microscopic states, and macro-locality,
defined by the metric which emerges from the low energy limit. As a result, the
low energy limit may suffer from a disordered locality characterized by
identifications of far away points. We argue that if such defects in locality
are rare enough they will be difficult to detect.Comment: 11 pages, 4 figures, revision with extended discussion of result
Conserved Quantities in Background Independent Theories
We discuss the difficulties that background independent theories based on
quantum geometry encounter in deriving general relativity as the low energy
limit. We follow a geometrogenesis scenario of a phase transition from a
pre-geometric theory to a geometric phase which suggests that a first step
towards the low energy limit is searching for the effective collective
excitations that will characterize it. Using the correspondence between the
pre-geometric background independent theory and a quantum information
processor, we are able to use the method of noiseless subsystems to extract
such coherent collective excitations. We illustrate this in the case of locally
evolving graphs.Comment: 11 pages, 3 figure
Evolution in Quantum Causal Histories
We provide a precise definition and analysis of quantum causal histories
(QCH). 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. We show that this local description of
evolution is sufficient and that unitary evolution can be recovered wherever it
should actually be expected. This formalism may describe a quantum cosmology
without an assumption of global hyperbolicity; it is thus more general than the
Wheeler-DeWitt approach. The structure of a QCH is also closely related to
quantum information theory and algebraic quantum field theory on a causal set.Comment: 20 pages. 8 figures. (v3: minor corrections, additional references
[2,3]) to appear in CQ
Nonperturbative dynamics for abstract (p,q) string networks
We describe abstract (p,q) string networks which are the string networks of
Sen without the information about their embedding in a background spacetime.
The non-perturbative dynamical formulation invented for spin networks, in terms
of causal evolution of dual triangulations, is applied to them. The formal
transition amplitudes are sums over discrete causal histories that evolve (p,q)
string networks. The dynamics depend on two free SL(2,Z) invariant functions
which describe the amplitudes for the local evolution moves.Comment: Latex, 12 pages, epsfig, 7 figures, minor change
Quantum gravity and the standard model
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. These are identified in terms of certain patterns of braiding of
graphs, thus giving a quantum gravitational foundation for the topological
preon model proposed by one of us.
These results apply to a large class of theories in which the Hilbert space
has a basis of states given by ribbon graphs embedded in a three-dimensional
manifold up to diffeomorphisms, and the dynamics is given by local moves on the
graphs, such as arise in the representation theory of quantum groups. For such
models, matter appears to be already included in the microscopic kinematics and
dynamics.Comment: 12 pages, 21 figures, improved presentation, results unchange
Trapped surfaces and emergent curved space in the Bose-Hubbard model
A Bose-Hubbard model on a dynamical lattice was introduced in previous work as a spin system analogue of emergent geometry and gravity. Graphs with regions of high connectivity in the lattice were identified as candidate analogues of spacetime geometries that contain trapped surfaces. We carry out a detailed study of these systems and show explicitly that the highly connected subgraphs trap matter. We do this by solving the model in the limit of no back-reaction of the matter on the lattice, and for states with certain symmetries that are natural for our problem. We find that in this case the problem reduces to a one-dimensional Hubbard model on a lattice with variable vertex degree and multiple edges between the same two vertices. In addition, we obtain a (discrete) differential equation for the evolution of the probability density of particles which is closed in the classical regime. This is a wave equation in which the vertex degree is related to the local speed of propagation of probability. This allows an interpretation of the probability density of particles similar to that in analogue gravity systems: matter inside this analogue system sees a curved spacetime. We verify our analytic results by numerical simulations. Finally, we analyze the dependence of localization on a gradual, rather than abrupt, falloff of the vertex degree on the boundary of the highly connected region and find that matter is localized in and around that region
Curved geometry and Graphs
Quantum Graphity is an approach to quantum gravity based on a background
independent formulation of condensed matter systems on graphs. We summarize
recent results obtained on the notion of emergent geometry from the point of
view of a particle hopping on the graph. We discuss the role of connectivity in
emergent Lorentzian perturbations in a curved background and the Bose--Hubbard
(BH) model defined on graphs with particular symmetries.Comment: are welcome. 4pp, 2 fig. Proceedings of Loops'11 Conference, Madri
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