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 gamma-matrices and a triple-spinor-field, called a triplet field, defined on the algebra. The algebra possesses three commutative sub-algebras which describe, respectively, the external space-time symmetry, the family structure and the internal color symmetry of quarks and leptons. The triplet field includes threefold (fourfold) repetitionary 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.
Algebraic description of external and internal attributes of fundamental fermions
为了描述基本费米子的外部和内部性质，在一个由狄拉克γ矩阵的所有三重直积组成的代数{ \it三重代数}上建立了一个多旋量场理论.将三元组代数分解为两个子代数的乘积，即一个外部代数和一个内部代数，这两个子代数分别与多旋量场{ \it三元组场}的外部特征和内部特征有关.与原Dirac代数$A_γ$同构的外代数的所有元素在置换群$S_3$的作用下是不变的，置换群$S_3$的作用是交换三重直积中$A_γ$元素的顺序。内部代数被分解为两个$4^2$维代数的乘积，称为族和色代数，它们描述了族和色的自由度。族和色代数具有精细的子结构，具有在$S_3$作用下不可约的“trio plus solo”构象。三重态场具有三重态加孤族模，其中包含普通三色夸克和无色孤轻子分量。为了结合温伯格-萨拉姆机制，需要引入两种类型的三重态场，即电弱等旋的左手二重态和右手单线态。在三重态场形式的内在机制中，可以自然地限定Yukawa相互作用，并对其耦合常数作出新的解释。普通的Higgs机制导致了一种新的Dirac质量矩阵，它可以在实验精度范围内解释夸克扇区的所有数据。
