Spacetime Algebra and Electron Physics

Abstract

This chapter presents a survey on the application of “geometric algebra” to the physics of electrons. Geometric algebra is the simplest and most coherent language available for mathematical physics and provides a single unified approach to a vast range of mathematical physics, and formulating and solving a problem in geometric algebra invariably leads to new physical insights. The chapter discusses aspects encompassing a wider range of topics relevant to electron physics. The idea that Clifford algebra provides the framework for a unified language for physics has been advocated most strongly by Hestenes, who is largely responsible for shaping the modern form of the subject. A list of some of the algebraic systems and techniques employed in modern theoretical physics (and especially particle physics) is presented in the chapter. The chapter focuses on the geometric algebra of spacetime—the spacetime algebra. The chapter explains that spacetime algebra, simiplifies the study of the Dirac theory, and discusses that the Dirac theory once formulated in the spacetime algebra is a powerful and flexible tool for the analysis of all aspects of electron physics—not just relativistic theory. The chapter begins with an introduction to the spacetime algebra (STA); concentrating on how the algebra of the STA is used to encode geometric ideas, such as lines, planes, and rotations.