Chris Doran

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The late 18th and 19th centuries were times of great mathematical progress. Many new mathematical systems and languages were introduced by some of the millenium's greatest mathematicians. Amongst these were the algebras of Cliiord (1878) and Grassmann (1877). While these algebras caused considerable interest at the time, they were largely abandoned with the(More)
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to programming complicated geometrical operations. But there is a fundamental weakness in this approach — the Euclidean(More)
This paper contains a tutorial introduction to the ideas of geometric algebra , concentrating on its physical applications. We show how the definition of a 'geometric product' of vectors in 2-and 3-dimensional space provides precise geometrical interpretations of the imaginary numbers often used in conventional methods. Reflections and rotations are(More)
We compute the spectrum of normalized 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 contributions give decay times for the various states, due to the absorption properties of the hole. As(More)
We discuss three applications of a gauge theory of gravity to rotating as-trophysical systems. The theory employs gauge fields in a flat Minkowski background spacetime to describe gravitational interactions. The iron fluo-rescence line observed in AGN is discussed, assuming that the line originates from matter in an accretion disk around a Kerr (rotating)(More)
The differential cross section for scattering of a Dirac particle in a black hole background is found. The result is the gravitational analog of the Mott formula for scattering in a Coulomb background. The equivalence principle is neatly embodied in the cross section, which depends only on the incident velocity, and not the particle mass. The low angle(More)