= Helicity content of a quantized Weyl field
{title2=$h_{\rm particle}=-\tfrac12,\quad h_{\rm antiparticle}=+\tfrac12$}
A left-handed massless <Weyl spinor> has a positive-energy <plane wave> transforming by $e^{i\alpha/2}$ under a rotation about its <momentum>. Its particle has <helicity> $-1/2$. The negative-frequency term multiplies an antiparticle <fermionic creation operator>, so its corresponding one-particle state carries the conjugate rotation phase and <helicity> $+1/2$. Thus a left-handed field has one particle and one antiparticle helicity; the right-handed field interchanges the signs. A full massless <Dirac field> contains both chiral fields and hence both particle helicities.
Back to article page
