Skew-Symmetric Linear Transformations and Electromagnetic Fields

Abstract

A charged particle in M is a triple (α, m, e), where (α,m) is a material particle and e is a nonzero real number called the charge of the particle. A free charged particle is a charged particle (α, m, e), where (α,m) is a free material particle. Charged particles do two things of interest to us. By their very presence they create electromagnetic fields and they also respond to the fields created by other charges. Our objective in this chapter is to isolate the appropriate mathematical object with which to model an electromagnetic field inM, derive many of its basic properties and then investigate these two activities.