A. Zee, Quantum Field Theory in a Nutshell · Problem VII.2.2
Field Theory Redux
Physics — QFT
Problem
Show that it is possible to stay with the SU(2) gauge group and to identify W3 as the photon A, but at the cost of inventing some experimentally unobserved lepton fields. This theory does not describe our world: For one thing, it is essentially impossible to incorporate the quarks. Show this! [Hint: We have to put the leptons into a triplet of SU(2) instead of a doublet.]