# Fermions with no mass, and helicity coupling.

1. May 2, 2010

### IRobot

Hi, I was reading a lecture of qft and I found that two equations:
\begin{flalign*} i \gamma^\mu \partial_\mu\psi_R - m\psi_L=0 \\ i \gamma^\mu \partial_\mu\psi_L - m\psi_R=0 \end{flalign*}
after splitting in two Dirac's equation with Weyl's projectors.
I found that really interesting that the coupling between the two chiralities is made by the mass term and that a massless fermion would have a symmetry U(1)xU(1) with one parameter for each helicity. But I would like to know if it has a much profound signification that the restriction to one symmetry is due to the mass.