ABSTRACT
In quantum field theory spin-12 particles are described by four-component wavefunctions ψ(x) (spinors) which obey the Dirac equation. The four independent components of ψ(x) correspond to particles and antiparticles with the two possible spin projections JZ = ±1/2 equivalent to the two helicities = ±1. Neutrinos as fundamental leptons are spin-12 particles like other fermions; however, it is an experimental fact that only left-handed neutrinos ( = −1) and right-handed antineutrinos ( = +1) are observed. Therefore, a two-component spinor description should, in principle, be sufficient (Weyl spinors). In a fourcomponent theory they are obtained by projecting out of a general spinor ψ(x) the components with = +1 for particles and = −1 for antiparticles with the help of the operators PL ,R = 12 (1 ∓ γ5). The two-component theory of the neutrinos will be discussed in detail later. Our discussion will be quite general, for a more extensive discussion see [Bjo64, Bil87, Kay89, Kim93,Sch97].
