Reconstructing the electro-weak theory from a gauge theory

Abstract

U(4) local transformations on the four Weyl spinors forming the isospin doublet of Dirac fermions are assumed as symmetries of the standard model. With the Lorentz transformations considered simultaneously, the symmetry group is enlarged in order to form a closed Lie algebra. In this framework, the chirality mixing gauge components with certain constraints collectively are identified as the Higgs field in the standard model. The scalar-appearance of the gauge-natured Higgs field and its varying coupling constants with the fermions, i.e. the mass-ratio parameters, are also given natural explanation. Additionally, a background of a constant right-handed gauge component is postulated to obtain the symmetry-breaking Higgs potential, which leads to a possible explanation of the parity violation in weak interactions. Further, the new framework provides an alternative perspective to understand the hyper symmetry U(1)Y , as a combination of a simultaneous phase rotation on both the left and right handed fermions and a rotation in the third direction of SU(2)R on the right-handed fermions. At last, a topological term involving the Higgs field is found to exist.