Weyl field

A spacetime field valued in one irreducible chiral spinor representation. A free massless left-handed Weyl field obeys $i({\partial }_t-\mathbf{\sigma }\cdot \nabla ){\chi }_L=0$. The left-handed massless plane-wave spinor and helicity content of a quantized Weyl field describe its modes and particle states. Field chirality fixes one spinor representation; it does not give the same particle and antiparticle helicity.