J. Barrett

Publications243
h-index51
Citations8,722
Highly Influential Citations528
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Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds
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…
Relativistic spin networks and quantum gravity
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…
Spherical Categories
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…
Lorentzian spin foam amplitudes: graphical calculus and asymptotics
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…
Holonomy and path structures in general relativity and Yang-Mills theory
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…
A Lorentzian signature model for quantum general relativity
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…
Finite element approximation of the p-Laplacian
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…
Asymptotic analysis of the EPRL four-simplex amplitude
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…
Invariants of piecewise-linear 3-manifolds
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…
Finite Element Approximation of the Cahn-Hilliard Equation with Degenerate Mobility
TLDR
A fully practical finite element approximation of the Cahn--Hilliard equation with degenerate mobility is considered, and it is shown well posedness and stability bounds for this approximation are shown.
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