A new framework for analysing the gravitational fields in a stationary, axisymmetric configuration is introduced. The method is used to construct a complete set of field equations for the vacuum region outside a rotating source. These equations are under-determined. Restricting … Continued
We review the applications of geometric algebra geometric algebra in electromagnetism, gravitation and multiparticle quantum systems. We discuss a gauge theory formulation of gravity and its implementation in geometric algebra, and apply this to the fermion bound state problem in … Continued
Anthony Lasenby’s keynote address at the SIGGRAPH 2003 conference in San Diego. PPT Movies
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 … Continued
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 … Continued
In this contribution we describe some applications of geometric algebra to the field of black hole physics. Our main focus is on the properties of Dirac wavefunctions around black holes. We show the existence of normalised bound state solutions, with … Continued
The Spacetime Algebra provides an elegant language for studying the Dirac equation. We show how to perform cross section calculations following a method suggested by Hestenes (1982). The S-matrix is replaced with an operator which rotates the initial states into … Continued
Recent developments in geometric algebra have shown that by moving from a projective to a conformal representation (5d representation of 3d space), one is able to extend the range of geometrical operations that can be carried out in an efficient … Continued
While the early applications of geometric algebra (GA) were confined to physics, there has been significant progress over recent years in applying geometric algebra to areas of engineering and computer science. The beauty of using the same language for these … Continued
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 Clifford (1878) and Grassmann (1877). While these … Continued