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

An unorthodox unified theory is developed to describe external and internal attributes and symmetries of fundamental fermions, quarks and leptons. Basic ingredients of the theory are an algebra which consists of all the triple-direct-products of Dirac γ-matrices and a triple-spinor-field, called a triplet field, defined on the algebra. The algebra possesses three commutative subalgebras which describe, respectively, the external spacetime symmetry, the family structure and the internal color symmetry of quarks and leptons. The triplet field includes threefold (fourfold) repetitional modes of spin 1/2 component fields with SU(3) (SU(4)) color symmetry. It is possible to qualify the Yukawa interaction and to make a new interpretation of its coupling constants naturally in an intrinsic mechanism of the triplet field formalism. The Dirac mass matrices with quasi-democratic structure are derived as an illustration.