Chirality, helicity and the weak interaction From what I'm understanding about Dirac spinors, using the Weyl basis for the $\gamma$ matrices the first two components behave as a left handed Weyl spinor, while the third and the fourth form a right handed Weyl spinor. By boosting in a direction or in the opposite, I can "asymptotically kill" either the left or right handed part of the (massive) spinor. Since only the left-handed part interacts with the weak force, does that mean that when I see an electron travelling very fast in one direction (same as/opposite to spin) I see/don't see it weakly interacting? This sounds very odd indeed.
I have two hypotheses:


*

*Massive spinors don't have an intrinsic chirality (since they are not eigenstates of chirality operator), the only information I have is about helicity, and the odd thing I described before is actually observed (really odd to me).

*Massive particles have an intrinsic chirality, but I don't see how the chirality information gets encoded into the Dirac spinor / how the weak interaction couples to only half of it. To me it seems that only the helicity information is carried by a spinor.

 A: You are correct that for a massive spinor, helicity is not Lorentz invariant. For a massless spinor, helicity is Lorentz invariant and coincides with chirality. Chirality is always Lorentz invariant.


*

*Helicity defined
$$
\hat h = \vec\Sigma \cdot \hat p,
$$
commutes with the Hamiltonian,
$$
[\hat h, H] = 0,
$$
but is clearly not Lorentz invariant, because it contains a dot product of a three-momentum.

*Chirality defined
$$
\gamma_5 = i\gamma_0 \ldots \gamma_3,
$$
is Lorentz invariant, but does not commute with the Hamiltonian,
$$
[\gamma_5, H] \propto m
$$
because a mass term mixes chirality, $m\bar\psi_L\psi_R$. If $m=0$, you can show from the massless Dirac equation that $\gamma_5 = \hat h$ when acting on a spinor.
Your second answer is closest to the truth:

The weak interaction couples only with left chiral spinors and is not frame/observer dependent.

A left chiral spinor can be written
$$
\psi_L = \frac12 (1+\gamma_5) \psi.
$$
If $m=0$, the left and right chiral parts of a spinor are independent. They obey separate Dirac equations. 
If $m\neq0$, the mass states $\psi$, 
$$
m(\bar\psi_R \psi_L + \bar\psi_L \psi_R) = m\bar\psi\psi\\
\psi = \psi_L + \psi_R
$$
are not equal to the interaction states, $\psi_L$ and $\psi_R$. There is a single Dirac equation for $\psi$ that is not separable into two equations of motion (one for $\psi_R$ and one for $\psi_L$).
If an electron, say, is propagating freely, it is a mass eigenstate, with both left and right chiral parts propagating.
