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
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
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
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
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
We discuss three applications of a gauge theory of gravity to rotating astrophysical systems. The theory employs gauge fields in a flat Minkowski background spacetime to describe gravitational interactions. The iron fluorescence line observed in AGN is discussed, assuming that … Continued
A lecture course in geometric algebra delivered at a summer school in Banff, Canada, 1996. A. N. Lasenby, C. J. L. Doran and S. F. Gull, Lectures in Geometric Algebra, In W. E. Baylis, editor, Clifford (Geometric) Algebras with Applications to Physics, Mathematics … Continued
Clifford’s ‘geometric algebra‘ is presented as the natural language for expressing geometrical ideas in mathematical physics. Its spacetime version ‘spacetime algebra‘ is introduced and is shown to provide a powerful, invariant description of relativistic physics. Applications to electromagnetism and gravitation … Continued