  A version of the Dirac equation is derived from first principles using a
combination of quaternions and multivariate 4-vectors. The nilpotent form of
the operators used allows us to derive explicit expressions for the
wavefunctions of free fermions, vector bosons, scalar bosons; Bose-Einstein
condensates, and baryons;annihilation, creation and vacuum operators; the
quantum field integrals; and C, P and T transformations; and to suggest new
insights into the meaning of supersymmetry and renormalization.
