Connes' gauge theory and Weinberg-Salam model of leptons on noncommutativespace-time

Connes' gauge theory is defined on noncommutative space-time. It is applied to formulate a noncommutative Weinberg-Salam (WS) model in the leptonic se ctor with nu (R). It is shown that the model has two Higgs doublets and a g auge boson sector after the Higgs mechanism contains the massive charged ga uge fields, two massless and two massive neutral gauge fields. It is also s hown that, at the tree level, the neutrino couples to one of two 'photons', the electron interacts with both 'photons', and there exists a nontrivial nu (R)-interaction on noncommutative space-time. To investigate the commuta tive limit of the model at the Lagrangian level, we generalize the charge c onjugation transformation in QED to that in noncommutative QED. We show tha t there are two different generalizations, the C and C' transformations, wh ich are based on two equivalent forms of the charge conjugation transformat ion in QED. It turns out that the two 'photons' are C' conjugates but becom e C conjugates (up to a sign) in the commutative limit. It is then proved t hat the bosonic action of the model has Z(2) symmetry, which reflects the C ' invariance in the bosonic sector. Our noncommutative WS model is reduced to the commutative WS theory at the Lagrangian level. Thus, in the neutral gauge boson sector, there are only one massless photon and one Z(o) in the commutative limit. This limit is studied by means of a theta -expansion, wh ich is obtained by expanding the action with respect to the noncommutativit y parameter.