The massless neutrinos can be represented by two component Weyl spinors. Then how does one say that it is an eigenstate of the chirality operator $\gamma^5$, which is a $4\times 4$ matrix and can act on $4\times 1$ column?
$\begingroup$
$\endgroup$
2
-
5$\begingroup$ Simply think of a Weyl Spinor as a Dirac spinor where the other two components are set to zero. Equivalently, a Weyl spinor (of chirality +1 belongs to the two-dimensional subspace with eigenvalue 1 under the action of the projection operator $P_+=\frac{(1-\gamma^5)}2$. $\endgroup$– sureshFeb 7, 2014 at 5:51
-
1$\begingroup$ @suresh Write this as an answer :) $\endgroup$– NeuneckFeb 7, 2014 at 9:53
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
1
Simply think of a Weyl Spinor as a Dirac spinor where the other two components are set to zero. Equivalently, a Weyl spinor (of chirality +1) belongs to the two-dimensional subspace with eigenvalue 1 under the action of the projection operator $P_+=\frac{(1-\gamma^5)}2$. For negative chirality, use the other projection operator, i.e., $P_-=\frac{(1+\gamma^5)}2$.
This is in response to @neuneck's suggestion though I don't understand the motivation for it. :-)
-
$\begingroup$ It's a full answer to the question, that's why! +1 $\endgroup$– NeuneckFeb 7, 2014 at 12:54