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
A series of lectures given at a joint Cambridge/MIT workshop on quantum computing. Lecture 1 – Introduction Lecture 2 – Quantum theory Lecture 3 – Dirac theory Lecture 4 – Further concepts
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
A reformulation of fermionic QFT in electromagnetic backgrounds is presented which uses methods analogous to those of conventional multiparticle quantum mechanics. Emphasis is placed on the (Schrodinger picture) states of the system, described in terms of Slater determinants of Dirac … Continued
In this paper we apply the concept of radar time (popularised by Bondi in his work on k-calculus) to the well-known relativistic twin `paradox’. Radar time is used to define hypersurfaces of simultaneity for a class of travelling twins, fr … 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
Talks on applications of geometric algebra, and more advanced topics in geometry, given at SIGGRAPH 2001. Applications of GA (PDF) Beyond Euclidean geometry (PDF)
new form of the Kerr solution is presented. The solution involves a time coordinate which represents the local proper time for free-falling observers on a set of simple trajectories. Many physical phenomena are particularly clear when related to this time … Continued
Geometric algebra provides a number of powerful tools for the treatment of rotations in three dimensions. Rotations are parameterised by rotors, which are normalised multivectors in a 4-d subalgebra of the 3-d geometric algebra. This parametrisation can be exploited to … Continued
J. Lasenby and A. Stevenson, Using geometric algebra in optical motion capture, In: E. Bayro and G. Sobczyk eds. Geometric algebra: a geometric approach to computer vision, neural and quantum computing, robotics and engineering. Birkhauser 2000. PDF