An objective account of the action of a Stern-Gerlach apparatus on spin-1/2 particles is given, using the Dirac equation. This generalizes earlier work on a causal interpretation of the Pauli equation to the relativistic domain, leading to a more natural … 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
A new gauge-theoretic approach to gravity is applied to the study of rotating cylindrically-symmetric strings. The interior and exterior equations are reduced to a simple set of first-order differential equations, and suitable matching conditions are obtained. The gauge theory formulation … Continued
This paper surveys the application of `geometric algebra’ to the physics of electrons. The mathematical ideas underlying geometric algebra were discovered jointly by Clifford and Grassmann in the late 19th century. Their discoveries were made during a period in which … Continued
A new gauge-theory description of gravity is presented, employing gauge fields in a flat background spacetime. These fields ensure that all physical relations are independent of the position and orientation of the matter fields in this background. The language of … Continued
Clifford algebras have been studied for many years and their algebraic properties are well known. In particular, all Clifford algebras have been classified as matrix algebras over one of the three division algebras. But Clifford Algebras are far more interesting … Continued
This paper contains a tutorial introduction to the ideas of geometric algebra, concentrating on its physical applications. We show how the definition of a `geometric product’ of vectors in 2- and 3-dimensional space provides precise geometrical interpretations of the imaginary … Continued
We present a reformulation of Grassmann calculus in terms of geometric algebra – a unified language for physics based on Clifford algebra. In this reformulation, Grassmann generators are replaced by vectors, so that every product of generators has a natural … Continued
It is shown that every Lie algebra can be represented as a bivector algebra; hence every Lie group can be represented as a spin group. Thus, the computational power of geometric algebra is available to simplify the analysis and applications … Continued
This paper employs the ideas of geometric algebra to investigate the physical content of Dirac’s electron theory. The basis is Hestenes’ discovery of the geometric significance of the Dirac spinor, which now represents a Lorentz transformation in spacetime. This transformation … Continued