Quaternionic electroweak theory and Cabibbo-Kobayashi-Maskawa matrix (Q1367621)

The paper begins with a brief review of some of the basic properties of the quaternionic electroweak theory, based on one-dimensional local gauge group \(U(1,q)_L/U(1,c)_\gamma\). In particular, the author discusses the complex scalar product, Dirac equation, complex projection of the Lagrangian, quaternionic Higgs field, and one-dimensional gauge group. The latter part of the paper is devoted to explain `quaternionic puzzle'' which appeared in the Leo and Rotelli version of the Salam-Weinberg model. The author suggests that this can be solved by introducing complex-barred mixing matrix with barred-quaternion for the right calculation of the real-valued parameters of Cabibbo-Kobayashi-Maskawa matrix by barred-quaternions.