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

The Role of National Debts in the Determination of the Yen-Dollar Exchange Rate

An intertemporal optimization model is developed to examine the determinants of the long-run nominal yen-dollar exchange rate in the presence of national debts. The model is tested empirically using data from Japan and the USA. The proposed theoretical specification is well supported by the data and shows that relative national debts as well as monetary and financial factors may play a significant role in the determination of the long-run nominal exchange rate between the yen and the dollar

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

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

Hadron Properties with FLIC Fermions

The Fat-Link Irrelevant Clover (FLIC) fermion action provides a new form of nonperturbative O(a)-improvement in lattice fermion actions offering near continuum results at finite lattice spacing. It provides computationally inexpensive access to the light quark mass regime of QCD where chiral nonanalytic behaviour associated with Goldstone bosons is revealed. The motivation and formulation of FLIC fermions, its excellent scaling properties and its low-lying hadron mass phenomenology are presented.Comment: 29 pages, 13 figures, 6 tables. Contribution to lecure notes in 2nd Cairns Topical Workshop on Lattice Hadron Physics 2003 (LHP 2003), Cairns, Australia, 22-30 Jul 200

Excited Baryons in Lattice QCD

We present first results for the masses of positive and negative parity excited baryons calculated in lattice QCD using an O(a^2)-improved gluon action and a fat-link irrelevant clover (FLIC) fermion action in which only the irrelevant operators are constructed with APE-smeared links. The results are in agreement with earlier calculations of N^* resonances using improved actions and exhibit a clear mass splitting between the nucleon and its chiral partner. An correlation matrix analysis reveals two low-lying J^P=(1/2)^- states with a small mass splitting. The study of different Lambda interpolating fields suggests a similar splitting between the lowest two Lambda1/2^- octet states. However, the empirical mass suppression of the Lambda^*(1405) is not evident in these quenched QCD simulations, suggesting a potentially important role for the meson cloud of the Lambda^*(1405) and/or a need for more exotic interpolating fields.Comment: Correlation matrix analysis performed. Increased to 400 configurations. 22 pages, 13 figures, 15 table

Numerical study of lattice index theorem usingimproved cooling and overlap fermions

We investigate topological charge and the index theorem on finite lattices numerically. Using mean field improved gauge field configurations we calculate the topological charge Q using the gluon field definition with ${\cal O}(a^4)$-improved cooling and an ${\cal O}(a^4)$-improved field strength tensor $F_{\mu\nu}$. We also calculate the index of the massless overlap fermion operator by directly measuring the differences of the numbers of zero modes with left- and right--handed chiralities. For sufficiently smooth field configurations we find that the gluon field definition of the topological charge is integer to better than 1% and furthermore that this agrees with the index of the overlap Dirac operator, i.e., the Atiyah-Singer index theorem is satisfied. This establishes a benchmark for reliability when calculating lattice quantities which are very sensitive to topology.Comment: 15 pages, 1 figure

Entanglement Entropy from a Holographic Viewpoint

The entanglement entropy has been historically studied by many authors in order to obtain quantum mechanical interpretations of the gravitational entropy. The discovery of AdS/CFT correspondence leads to the idea of holographic entanglement entropy, which is a clear solution to this important problem in gravity. In this article, we would like to give a quick survey of recent progresses on the holographic entanglement entropy. We focus on its gravitational aspects, so that it is comprehensible to those who are familiar with general relativity and basics of quantum field theory.Comment: Latex, 30 pages, invited review for Classical and Quantum Gravity, minor correction