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
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
This paper presents an intuitive geometric model for multiqubit quantum systems, which is formulated using geometric (aka Clifford) algebras. First, it is shown how Euclidean spinors may be interpreted as entities in the geometric algebra of a Euclidean vector space. … Continued
We consider topological contributions to the action integral in a gauge theory formulation of gravity. Two topological invariants are found and are shown to arise from the scalar and pseudoscalar parts of a single integral. Neither of these action integrals … Continued
The Spacetime Algebra provides an elegant language for studying the Dirac equation. Cross section calculations can be performed in an intuitive way following a method suggested by Hestenes. The S-matrix is replaced with an operator which rotates the initial states … Continued