  In a recent publication the I showed how the geometric algebra ${G}_{4,1}$,
the algebra of 5-dimensional space-time, can generate relativistic dynamics
from the simple principle that only null geodesics should be allowed. The same
paper showed also that Dirac equation could be derived from the condition that
a function should be monogenic in that algebra; this construction of the Dirac
equation allows a choice for the imaginary unit and it was suggested that
different imaginary units could be assigned to the various elementary
particles. An earlier paper had already shown the presence of standard model
gauge group symmetry in complexified ${G}_{1,3}$, an algebra isomorphic to
${G}_{4,1}$.
  In this presentation I explore the possible choices for the imaginary unit in
the Dirac equation to show that SU(3) and SU(2) symmetries arise naturally from
such choices. The quantum numbers derived from the imaginary units are unusual
but a simple conversion allows the derivation of electric charge and isospin,
quantum numbers for two families of particles. This association to elementary
particles is not final because further understanding of the role played by the
imaginary unit is needed.
