Geometric Algebra in 3 Dimensions In this lecture we explore the consequences of our definition of the geometric product in three dimensions. We find that Hamilton’s quaternions arise naturally in the geometric algebra of three dimensions, but that the generators … Continued
Geometric Algebra in 2 Dimensions In this lecture we introduce geometric algebra through studying various products of vectors. Our goal is to find an associative, invertible product that allows us to multiply together two vectors. Complex arithmetic helps motivate the … Continued
This year I am giving a new course on Geometric Algebra as part of the Masters Course in Scientific Computing at Cambridge University. This course is run by the Doctoral Training Centre in Scientific Computing, in the Physics Department at … Continued
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
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
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
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
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
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