Algebraic description of external and internal attributes of fundamental fermions

摘要

To describe external and internal attributes of fundamental fermions, a theory of multi-spinor fields is developed on an algebra, a triplet algebra, which consists of all the triple-direct-products of Dirac γ-matrices. The triplet algebra is decomposed into the product of two subalgebras, an external algebra and an internal algebra, which are exclusively related with external and internal characteristic of the multi-spinor field named triplet fields. All elements of the external algebra which is isomorphic to the original Dirac algebra A_γ are invariant under the action of permutation group S_3 which works to exchange the order of the A_γ elements in the triple-direct-product. The internal algebra is decomposed into the product of two 4~2 dimensional algebras, called the family and color algebras, which describe the family and color degrees of freedom. The family and color algebras have fine substructures with "trio plus solo" (3+1) conformations which are irreducible under the action of S_3. The triplet field has trio plus solo family modes with ordinary tricolor uark and colorless solo lepton components. To incorporate the Weinberg-Salam mechanism, it is re uired to introduce two types of triplet fields, a left-handed doublet and right-handed singlets of electroweak iso-spin. It is possible to ualify the Yukawa interaction and to make a new interpretation of its coupling constants naturally in an intrinsic mechanism of the triplet field formalism. The ordinary Higgs mechanism leads to the Dirac mass matrices which can explain all data of uark sector within experimental accuracy.