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
It is argued that geometric algebra, in the form of the multiparticle spacetime algebra, is well-suited to the study of multiparticle quantum theory, with advantages over conventional techniques both in ease of calculation and in providing an intuitive geometric understanding … Continued
A new method for modelling spherically symmetric inhomogeneities is applied to the formation of clusters in an expanding Universe. We impose simple initial velocity and density perturbations of finite extent and we investigate the subsequent evolution of the density field. … Continued
A new method is proposed for modelling spherically symmetric inhomogeneities in the Universe. The inhomogeneities have finite size and are compensated, so they do not exert any measurable gravitational force beyond their boundary. The region exterior to the perturbation is … Continued
A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the position and orientation of the matter fields. … Continued
We discuss a coordinate-free approach to the geometry of computer vision problems. The technique we use to analyse the 3-dimensional transformations involved will be that of geometric algebra: a framework based on the algebras of Clifford and Grassmann. This is … Continued
Stationary vacuum solutions of Kerr-Schild type are analysed within the framework of gauge-theory gravity. The complex structure at the heart of these fields is shown to have a clear geometric origin, with the role of the unit imaginary fulfilled by … Continued