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
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
Recent Applications of Conformal Geometric Algebra
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
Bound states and decay times of fermions in a Schwarzschild black hole background
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
Conformal models of de Sitter space, initial conditions for inflation and the CMB
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