404 citations · 3.5k across the 79 of their papers we have counts for
30 papers · 1 filter
Spectral estimators for finite non-commutative geometries
John W. Barrett, Paul Druce, Lisa Glaser
A finite non-commutative geometry consists of a fuzzy space together with a Dirac operator satisfying the axioms of a real spectral triple. This paper addreses the question of how…
Tullio Regge's legacy: Regge calculus and discrete gravity
John W. Barrett, Daniele Oriti, Ruth M. Williams
The review paper "Discrete Structures in Physics", written in 2000, describes how Regge's discretization of Einstein's theory has been applied in classical relativity and quantum g…
Monte Carlo simulations of random non-commutative geometries
John W. Barrett, Lisa Glaser
Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with…
Gauge gravity and discrete quantum models
John W. Barrett, Steven Kerr
The gauge gravity action for general relativity in any dimension using a connection for the Euclidean or Poincaré group and a symmetry-breaking scalar field is written using a part…
Holonomy observables in Ponzano-Regge type state sum models
John W. Barrett, Frank Hellmann
We study observables on group elements in the Ponzano-Regge model. We show that these observables have a natural interpretation in terms of Feynman diagrams on a sphere and contras…
Asymptotics of 4d spin foam models
John W. Barrett, Richard J. Dowdall, Winston J. Fairbairn +3
We study the asymptotic properties of four-simplex amplitudes for various four-dimensional spin foam models. We investigate the semi-classical limit of the Ooguri, Euclidean and Lo…
Quantum gravity asymptotics from the SU(2) 15j symbol
John W. Barrett, Winston J. Fairbairn, Frank Hellmann
The asymptotics of the SU(2) 15j symbol are obtained using coherent states for the boundary data. The geometry of all non-suppressed boundary data is given. For some boundary data,…
A Summary of the asymptotic analysis for the EPRL amplitude
John W. Barrett, Richard J. Dowdall, Winston J. Fairbairn +2
We review the basic steps in building the asymptotic analysis of the Euclidean sector of new spin foam models using coherent states, for Immirzi parameter less than one. We focus o…
Lorentzian spin foam amplitudes: graphical calculus and asymptotics
John W. Barrett, Richard J. Dowdall, Winston J. Fairbairn +2
The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics…
Asymptotic analysis of the EPRL four-simplex amplitude
John W. Barrett, R. J. Dowdall, Winston J. Fairbairn +2
The semiclassical limit of a 4-simplex amplitude for a spin foam quantum gravity model with an Immirzi parameter is studied. If the boundary state represents a non-degenerate 4-sim…
The Ponzano-Regge model
John W. Barrett, Ileana Naish-Guzman
The definition of the Ponzano-Regge state-sum model of three-dimensional quantum gravity with a class of local observables is developed. The main definition of the Ponzano-Regge mo…
The Ponzano-Regge model and Reidemeister torsion
John W. Barrett, Ileana Naish-Guzman
The Ponzano-Regge model of three-dimensional quantum gravity is well-defined when the observables satisfy a certain condition involving the twisted cohomology. In this case, the pa…
Feynman diagams coupled to three-dimensional quantum gravity
John W. Barrett
A framework for quantum field theory coupled to three-dimensional quantum gravity is proposed. The coupling with quantum gravity regulates the Feynman diagrams. One recovers the us…
Feynman loops and three-dimensional quantum gravity
John W. Barrett
This paper explores the idea that within the framework of three-dimensional quantum gravity one can extend the notion of Feynman diagram to include the coupling of the particles in…
Asymptotics of Relativistic Spin Networks
John W Barrett, Christopher M Steele
The stationary phase technique is used to calculate asymptotic formulae for SO(4) Relativistic Spin Networks. For the tetrahedral spin network this gives the square of the Ponzano-…
Geometrical measurements in three-dimensional quantum gravity
John W. Barrett
A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmo…
Integrability for Relativistic Spin Networks
John C. Baez, John W. Barrett
The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin networ…
Refractive gravitational waves and quantum fluctuations
John W. Barrett
Refractive gravitational waves are a generalisation of impulsive waves on a null hypersurface in which the metric is discontinuous but a weaker continuity condition for areas holds…
State sum models for quantum gravity
John W. Barrett
This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combi…
A Lorentzian Signature Model for Quantum General Relativity
John W. Barrett, Louis Crane
We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for th…
The Quantum Tetrahedron in 3 and 4 Dimensions
John C. Baez, John W. Barrett
Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points corres…
The asymptotics of an amplitude for the 4-simplex
John W. Barrett, Ruth M. Williams
An expression for the oscillatory part of an asymptotic formula for the relativistic spin network amplitude for a 4-simplex is given. The amplitude depends on specified areas for e…
A note on area variables in Regge calculus
John W. Barrett, Martin Rocek, Ruth M. Williams
We consider the possibility of setting up a new version of Regge calculus in four dimensions with areas of triangles as the basic variables rather than the edge-lengths. The diffic…
Relativistic spin networks and quantum gravity
John W. Barrett, Louis Crane
Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) times SU(2). Relativistic quantum spins are related to the geometry of the 2-dimen…