New Algebraic Unified Theory of Leptons and Quarks

概要

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A new algebraic theory is developed to describe the characteristic features of leptons and quarks as a whole. A pair of master fields with up and down weak-isospin is introduced and postulated to obey the generalized Dirac Equations with coefficient matrices which belong to an algebra, a triplet algebra, consisting of triple-direct-products of Dirac's γ-matrices. The triplet algebra is decomposed into three subalgebras, in a non-intersecting manner, which describe respectively the external Lorentz symmetry, the internal colour symmetry and the degrees of freedom for fourfold-family-replication of fundamental fermionic particle modes. The master fields belonging to a 64 dimensional multi-spinor space form non-irreducible representations of the Lorent group and represent fourfold replications of families of spin 1/2 particles, each one of which accomodates triply-degenerate quark modes and singlet leptonic modes. Canonical quantization of master fields leads naturally to the renormalizable unified field theories of fundamental fermions with universal gauge interactions of local symmetries having the route of decent from SU_c(4)×SU_L(2)×SU_R(2) to SU_c(3)×SU_L(2)×U_Y(1).
理論物理学刊行会の論文
1987-08-25