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 mathematicians were uncovering many new algebraic structures (quaternions, matrices, groups, etc.) and the full potential of Clifford and Grassmann’s work was lost as mathematicians concentrated on its algebraic properties. This problem was exacerbated by Clifford’s early death and Grassmann’s lack of recognition during his lifetime. This paper is part of a concerted effort to repair the damage caused by this historical accident. We firmly believe that geometric algebra is the simplest and most coherent language available for mathematical physics, and deserves to be understood and used by the physics and engineering communities. Geometric algebra provides a single, unified approach to a vast range of mathematical physics, and formulating and solving a problem in geometric algebra invariably leeds to new physical insights. In the a series of earlier papers geometric algebra techniques were applied to number of areas of physics, including relativistic electrodynamics and Dirac theory. In this paper we extend aspects of that work to encompass a wider range of topics relevant to electron physics. We hope that the work presented here makes a convincing case for the use of geometric algebra in electron physics.
Chris Doran, Anthony Lasenby, Stephen Gull, Shyamal Somaroo and Anthony Challinor, Spacetime Algebra and Electron Physics, In P. W. Hawkes, editor, Advances in Imaging and Electron Physics, Vol. 95, p. 271-386 (Academic Press, 1996)