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1 Jan 2005

Conformal Geometry and the Universe

by Anthony Lasenby | posted in: Conference Proceedings | 0

The conformal approach to Euclidean geometry introduced by David Hestenes, uses null vectors in an enlarged space to represent points. Here we show how these same techniques can be extended to the curved spacetimes relevant in cosmology. An extended example … Continued

1 Jan 2005

Integral equations, Kerr-Schild fields and gravitational sources

by Chris Doran | posted in: Report | 0

Kerr-Schild solutions to the vacuum Einstein equations are considered from the viewpoint of integral equations. We show that, for a class of Kerr-Schild fields, the stress-energy tensor can be regarded as a total divergence in Minkowski spacetime. If one assumes … Continued

1 Jan 2005

Fermion absorption cross section of a Schwarzschild black hole

by Chris Doran | posted in: Journal Paper | 0

We study the absorption of massive spin-half particles by a small Schwarzschild black hole by numerically solving the single-particle Dirac equation in Painleve-Gullstrand coordinates. We calculate the absorption cross section for a range of gravitational couplings Mm/m_P^2 and incident particle … Continued

1 Jan 2005

Applications of Conformal Geometric Algebra in Computer Vision and Graphics

by Chris Doran | posted in: Conference Proceedings | 0

This paper introduces the mathematical framework of conformal geometric algebra (CGA) as a language for computer graphics and computer vision. Specifically it discusses a new method for pose and position interpolation based on CGA which firstly allows for existing interpolation … Continued

1 Jan 2005

Recent Applications of Conformal Geometric Algebra

by Anthony Lasenby | posted in: Conference Proceedings | 0

We discuss a new covariant approach to geometry, called conformal geometric algebra, concentrating particularly on applications to projective geometry and new hybrid geometries. In addition, a new method of working, which can achieve similar results, but using only one extra … Continued

1 Jan 2005

Bound states and decay times of fermions in a Schwarzschild black hole background

by Anthony Lasenby | posted in: Journal Paper | 0

We compute the spectrum of normalizable fermion bound states in a Schwarzschild black hole background. The eigenstates have complex energies. The real part of the energies, for small couplings, closely follow a hydrogen-like spectrum. The imaginary parts give decay times … Continued

1 Jan 2004

Conformal models of de Sitter space, initial conditions for inflation and the CMB

by Anthony Lasenby | posted in: Conference Proceedings | 0

Conformal embedding of closed-universe models in a de Sitter background suggests a quantisation condition on the available conformal time. This condition implies that the universe is closed at no greater than the 10% level. When a massive scalar field is … Continued

1 Jan 2004

Circle and sphere blending with conformal geometric algebra

by Chris Doran | posted in: Report | 0

Blending schemes based on circles provide smooth `fair’ interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity can be achieved by … Continued

1 Jan 2004

A Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra of a 6-D Euclidean Vector Space

by Chris Doran | posted in: Conference Proceedings | 0

Geometric algebra is a mathematical structure that is inherent in any metric vector space, and defined by the requirement that the metric tensor is given by the scalar part of the product of vectors. It provides a natural framework in … Continued

1 Jan 2004

Single-qubit gates and measurements in the surface acoustic wave quantum computer

by Chris Doran | posted in: Journal Paper | 0

In the surface acoustic wave quantum computer, the spin state of an electron trapped in a moving quantum dot comprises the physical qubit of the scheme. Via detailed analytic and numerical modeling of the qubit dynamics, we discuss the effect … Continued

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