The family problem

The group theoretical approach to the family problem is discussed. Fermions are unified into an irreducible representation of a simple gauge. The orthogonal groups are automatically anomaly-free and admit spinorial representations. A spinor does not decompose into exact replicas as desired. The group theoretic structure is sufficiently suggestive as to warrant some serious efforts to somehow conceal the V + A fermions from view. The most obvious way is to introduce Higgs to give large masses to the unwanted V + A fermions. The idea of technicolor (TC) was introduced by Gell-Mann et al. The fundamental hypothesis of technicolor, that TC non-singlets are confined by techni-strong forces, was then invoked to conceal the V + A fermions. The technicolor scheme is explained in this paper. The group theory of orthogonal groups strongly suggests the natural incorporation of the observed repetitive family structure. (Kato, T.)