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An unorthodox unified theory is developed to describe external and internalattributes and symmetries of fundamental fermions, quarks and leptons. Basicingredients of the theory are an algebra which consists of all thetriple-direct-products of Dirac gamma-matrices and a triple-spinor-field,called a triplet field, defined on the algebra. The algebra possesses threecommutative sub-algebras which describe, respectively, the external space-timesymmetry, the family structure and the internal color symmetry of quarks andleptons. The triplet field includes threefold (fourfold) repetitionary modes ofspin 1/2 component fields with SU(3) (SU(4)) color symmetry. It is possible toqualify the Yukawa interaction and to make a new interpretation of its couplingconstants naturally in an intrinsic mechanism of the triplet field formalism.The Dirac mass matrices with quasi-democratic structure are derived as anillustration.

Unified theory for external and internal attributes and symmetries of fundamental fermions