Third-order equation for two-component spinors

We present the properties of a two-component spinor field that obeys a third-order equation. It is separated into a massive part that corresponds closely to a Dirac field, and a massless part that obeys the Weyl equation. We discuss the interaction of such a field with an external electromagnetic field and the (weak) interactions of two such fields. They can be considered both in terms of relativistic quantum mechanics and quantum field theory. We conclude that this formulation has some attractive features, such as a unified treatment of electrons and muons with their neutrinos, a special role of thePC transformation, a more convergent propagator and a new approach to interactions. It also has some serious difficulties, aside from those generally associated with higher-order equations. These are mainly related to inconsistencies in the simultaneous considerations of electromagnetic and weak interactions. The approach also suggests a further unification of the electron and muon fields into a single bispinor field.