  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.
