Connes' Gauge Theory on Noncommutative Space-Times

TL;DR

This paper formulates a noncommutative version of the GWS model using Connes' gauge theory, revealing novel features such as two Higgs doublets and unique gauge boson interactions, which reduce to the standard model in the commutative limit.

Contribution

It introduces a noncommutative GWS model based on Connes' gauge theory, highlighting new gauge boson structures and interactions not present in the standard model.

Findings

The model contains two Higgs doublets.

Gauge boson sector includes massive charged and neutral bosons.

Neutrino couples to one of two 'photons' and exhibits nontrivial interactions.

Abstract

Connes' gauge theory is defined on noncommutative space-times. It is applied to formulate a noncommutative Glashow-Weinberg-Salam (GWS) model in the leptonic sector. It is shown that the model has two Higgs doublets and the gauge bosons sector after the Higgs mechanism contains the massive charged gauge fields, two massless and two massive neutral gauge fields. It is also shown that, in the tree level, the neutrino couples to one of two `photons', the electron interacts with both `photons' and there occurs a nontrivial $\nu_R$-interaction on noncommutative space-times. Our noncommutative GWS model is reduced to the GWS theory in the commutative limit. Thus in the neutral gauge bosons sector there are only one massless photon and only one $Z^0$ in the commutative limit.