Fermions with no mass, and helicity coupling.

[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.

 

[azntoon]

The two equations you mention are known as the Dirac equations, and they are a cornerstone of quantum field theory. The fact that a mass term is responsible for the coupling between the left- and right-handed components of the fermion is an important insight, since it implies that a massless fermion would be symmetric under U(1)xU(1). This has far-reaching implications, as it suggests that the mass of a particle may be related to its interaction with other particles in the standard model. Furthermore, this insight can also be used to explain certain experimental observations, such as the observed masses of neutrinos.