New Basis for the Standard Model for Electroweak Interactions

Abstract

The standard model for electroweak interactions uses the concepts of weak hypercharge and local gauge invariance of the Lagrangian density under the gauge group SU(2) x U(1). Taylor has remarked that U(1), being a multiply-connected group, in general, should have different coupling strengths for singlets and doublets. But in the development of the standard model, even for U(1), the coupling strength has been taken to be the same for all the multiplets without a priori justification. Wilczek has pointed out that the assignment of hypercharge values to left- and right-handed leptons and quarks is very peculiar. However, no solution has been provided. Ellis has also reservations for the rather bizarre set up of group representations and hypercharges. It has also been noticed that, in addition to the above weak points of the model, the generator of the group U(1) is changed at different stages during a single analysis. In this paper, a new basis is provided that avoids these peculiar and odd concepts and hypercharge assignments, and a satisfactory solution is given for the first time. This is done by generalising the expression for the transformation law for 4-vector potential in electromagnetism. It gives exactly the same results as obtained in the standard model for electroweak interactions.