Abstract
Dirac's square root procedure, when extended to the reducible representations of Dirac algebra (defined by Clifford algebras) and combined with an intrinsic exclusion principle, leads successfully (within the standard model) to three families of leptons and quarks and, in addition, to two families of not-yet-observed fundamental scalars. Among these, the coloured scalars imply new (generally unstable) hadronic states of five types.
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