## Current issues in real-time graphics

Talk delivered at AGACSE 2010 on “Thoughts from the front line: Current issues in real-time graphics and areas where Geometric Algebra can help”. PPT

## Geometric Algebra and Physics

Introductory talk on Geometric Algebra by Anthony Lasenby given to the Oxford Undergraduate Physics Conference in 2008. PDF

## Geometric Algebra for Physicists

This book is available from CUP and Amazon. Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with … Continued

## Analytic solutions to Riemann-squared gravity with background isotropic torsion

Motivated by conventional gauge theories, we consider a theory of gravity in which the Einstein-Hilbert action is replaced by a term that is quadratic in the Riemann tensor. We focus on cosmological solutions to the field equations in flat, open … Continued

## Minimax determination of the energy spectrum of the Dirac equation in a Schwarzschild background

We calculate the bound-state energy spectrum of the Dirac Equation in a Schwarzschild black hole background using a minimax variational method. Our method extends that of Talman to the case of non-Hermitian interactions, such as a black hole. The trial … Continued

## Closed Universes, de Sitter Space and Inflation

We present a new approach to constructing inflationary models in closed universes. 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 … Continued

## Conformal Geometry and the Universe

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

## Integral equations, Kerr-Schild fields and gravitational sources

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

## Fermion absorption cross section of a Schwarzschild black hole

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