ABSTRACT
The world we see is Poincare invariant. It also has internal symmetries—both global and local—the latter giving rise to interactions (forces) described by gauge theories. The primary tool is the Clifford algebra. This chapter introduces the anticommutator, where the Dirac matrices have a unique representation (up to equivalence) as 4 × 4 matrices. By alternately forming commutators and anticommutators we find all 16 independent matrices. The chapter suggests that the translations commute, and form a vector representation of the homogeneous Lorentz group whose generators satisfy the algebra in the final line. It looks for a complete commuting set of observables and distinguish the massive and massless cases. The chapter also considers the transformations of Dirac four-component spinors under the Lorentz group.
