  Many difficulties of interpretation met by contemporary researchers
attempting to recast or generalize Dirac's, Proca's, or Maxwell's theories
using biquaternions or Clifford numbers have been encountered long ago by a
number of physicists including Lanczos, Proca, and Einstein. In the modern
approach initiated by Gursey, these difficulties are solved by recognizing that
most generalizations lead to theories describing superpositions of particles of
different intrinsic spin and isospin, so that the correct interpretation
emerges from the requirement of full Poincare covariance, including space and
time reversal, as well as of reversion and gauge invariance. For instance, the
doubling of the number of solutions implied by the simplest generalization of
Dirac's equation (i.e., Lanczos's equation) can be interpreted as isospin. In
this approach, biquaternions and Clifford numbers become powerful opportunities
to formulate the Standard Model of elementary particles, as well as many of its
possible generalizations, in very elegant and compact ways.
