245 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
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
Network Codes for Real-Time Applications
We consider the scenario of broadcasting for real-time applications and loss
recovery via instantly decodable network coding. Past work focused on
minimizing the completion delay, which is not the right objective for real-time
applications that have strict deadlines. In this work, we are interested in
finding a code that is instantly decodable by the maximum number of users.
First, we prove that this problem is NP-Hard in the general case. Then we
consider the practical probabilistic scenario, where users have i.i.d. loss
probability and the number of packets is linear or polynomial in the number of
users. In this scenario, we provide a polynomial-time (in the number of users)
algorithm that finds the optimal coded packet. The proposed algorithm is
evaluated using both simulation and real network traces of a real-time Android
application. Both results show that the proposed coding scheme significantly
outperforms the state-of-the-art baselines: an optimal repetition code and a
COPE-like greedy scheme.Comment: ToN 2013 Submission Versio
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
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
A discrete, unitary, causal theory of quantum gravity
A discrete model of Lorentzian quantum gravity is proposed. The theory is
completely background free, containing no reference to absolute space, time, or
simultaneity. The states at one slice of time are networks in which each vertex
is labelled with two arrows, which point along an adjacent edge, or to the
vertex itself. The dynamics is specified by a set of unitary replacement rules,
which causally propagate the local degrees of freedom. The inner product
between any two states is given by a sum over histories. Assuming it converges
(or can be Abel resummed), this inner product is proven to be hermitian and
fully gauge-degenerate under spacetime diffeomorphisms. At least for states
with a finite past, the inner product is also positive. This allows a Hilbert
space of physical states to be constructed.Comment: 38 pages, 9 figures, v3 added to exposition and references, v4
expanded prospects sectio
A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime
We present a toy model for interacting matter and geometry that explores
quantum dynamics in a spin system as a precursor to a quantum theory of
gravity. The model has no a priori geometric properties, instead, locality is
inferred from the more fundamental notion of interaction between the matter
degrees of freedom. The interaction terms are themselves quantum degrees of
freedom so that the structure of interactions and hence the resulting local and
causal structures are dynamical. The system is a Hubbard model where the graph
of the interactions is a set of quantum evolving variables. We show
entanglement between spatial and matter degrees of freedom. We study
numerically the quantum system and analyze its entanglement dynamics. We
analyze the asymptotic behavior of the classical model. Finally, we discuss
analogues of trapped surfaces and gravitational attraction in this simple
model.Comment: 23 pages, 6 figures; updated to published versio
Quantum Bose-Hubbard model with an evolving graph as a toy model for emergent spacetime
We present a toy model for interacting matter and geometry that explores quantum dynamics in a spin system as a precursor to a quantum theory of gravity. The model has no a priori geometric properties; instead, locality is inferred from the more fundamental notion of interaction between the matter degrees of freedom. The interaction terms are themselves quantum degrees of freedom so that the structure of interactions and hence the resulting local and causal structures are dynamical. The system is a Hubbard model where the graph of the interactions is a set of quantum evolving variables. We show entanglement between spatial and matter degrees of freedom. We study numerically the quantum system and analyze its entanglement dynamics. We analyze the asymptotic behavior of the classical model. Finally, we discuss analogues of trapped surfaces and gravitational attraction in this simple model
Homogeneous Chemoselective Hydrogenation of Heterocyclic Compounds – The Case of 1,4 Addition on Conjugated C-C and C-O Double Bonds of Arylidene Tetramic Acids
Quantum Histories and Quantum Gravity
This paper reviews the histories approach to quantum mechanics. This
discussion is then applied to theories of quantum gravity. It is argued that
some of the quantum histories must approximate (in a suitable sense) to
classical histories, if the correct classical regime is to be recovered. This
observation has significance for the formulation of new theories (such as
quantum gravity theories) as it puts a constraint on the kinematics, if the
quantum/classical correspondence principle is to be preserved. Consequences for
quantum gravity, particularly for Lorentz symmetry and the idea of "emergent
geometry", are discussed.Comment: 35 pages (29 pages main body), two figure
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