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Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds

- J. Barrett
- Physics
- 5 July 1994

I used to keep the entire spin networks literature in a small folder on my shelf. The recent explosion of interest in the subject has made this impossible; more is probably now written every week… Expand

Relativistic spin networks and quantum gravity

- J. Barrett, L. Crane
- Physics
- 12 September 1997

Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2)×SU(2). Relativistic quantum spins are related to the geometry of the two-dimensional faces of a… Expand

Spherical Categories

- J. Barrett, B. W. Westbury
- Physics, Mathematics
- 25 October 1993

This paper is a study of monoidal categories with duals where the tensor product need not be commutative. The motivating examples are categories of representations of Hopf algebras. We introduce the… Expand

Lorentzian spin foam amplitudes: graphical calculus and asymptotics

- J. Barrett, R. J. Dowdall, W. Fairbairn, F. Hellmann, R. Pereira
- Physics, Mathematics
- 14 July 2009

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 of this amplitude… Expand

Holonomy and path structures in general relativity and Yang-Mills theory

- J. Barrett
- Mathematics
- 1 September 1991

This article is about a different representation of the geometry of the gravitational field, one in which the paths of test bodies play a crucial role. The primary concept is the geometry of the… Expand

A Lorentzian signature model for quantum general relativity

- J. Barrett, L. Crane
- Physics
- 9 April 1999

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 the path integral… Expand

Finite element approximation of the p-Laplacian

- J. Barrett, Wenbin Liu
- Mathematics
- 13 January 1993

In this paper we consider the continuous piecewise linear finite el- ement approximation of the following problem: Given p € (1, oo), /, and g , find u such that -V • (\Vu\"-2Vu) = f iniicR2, u = g… Expand

Asymptotic analysis of the EPRL four-simplex amplitude

- J. Barrett, R. J. Dowdall, W. Fairbairn, H. Gomes, F. Hellmann
- Physics
- 6 February 2009

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-simplex geometry, the… Expand

Invariants of piecewise-linear 3-manifolds

- J. Barrett, B. W. Westbury
- Physics, Mathematics
- 25 November 1993

In this paper we develop a theory for constructing an invariant of closed oriented 3-manifolds, given a certain type of Hopf algebra. Examples are given by a quantised enveloping algebra of a… Expand

Finite Element Approximation of the Cahn-Hilliard Equation with Degenerate Mobility

- J. Barrett, J. F. Blowey, H. Garcke
- Mathematics, Computer ScienceSIAM J. Numer. Anal.
- 1 November 1999

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