A demonstration that electroweak theory can violate parity automatically (leptonic case)

Abstract

We bring to light an electroweak model which has been reappearing in the literature under various guises, [1-5]. In this model, weak isospin is shown to act automatically on states of only a single chirality (left). This is achieved by building the model exclusively from the raising and lowering operators of the Clifford algebra Cl(4). That is, states constructed from these ladder operators mimic the behaviour of left- and right-handed electrons and neutrinos under unitary ladder operator symmetry. This ladder operator symmetry is found to be generated uniquely by su(2)_L and u(1)_Y . Crucially, the model demonstrates how parity can be maximally violated, without the usual step of introducing extra gauge and extra Higgs bosons, or ad hoc projectors.