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
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this entanglement … Continued
The multiparticle spacetime algebra (MSTA) is an extension of Dirac theory to a multiparticle setting, which was first studied by Doran, Gull and Lasenby. The geometric interpretation of this algebra, which it inherits from its one-particle factors, possesses a number … Continued
Systems of partial differential equations lie at the heart of physics. Despite this, the general theory of these systems has remained rather obscure in comparison to numerical approaches such as finite element models and various other discretisation schemes. There are, … 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
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
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