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3

Frankly I find this so-called pedagogical article quite unintelligible and fail to see what the author wanted to say about these two operations. I also can't make any sense of the "derivation" of 7.3 based on the chiral projection being a "numerical matrix" and therefore commuting with charge conjugation operator. Moreso the remark: Elaborate statements ...


4

I think your problem is mostly a problem of notation. If you write two Weyl spinors inside a Dirac spinor, you should use different symbols to avoud confusion, i.e. $$\psi = \begin{pmatrix} \xi_L \\ i \sigma_2 \xi_L^* \end{pmatrix}.$$ Now, your object $\Psi$ has a left-chiral component $\xi_L$ and a right-chiral component $i \sigma_2 \xi_L^*$. (A Dirac ...


3

We define positive chirality to be right-handed. Ultimately, this was an arbitrary sign choice (like the choice of which charges are negative versus positive), and (like the choice of charge sign) it was probably not the best choice. However, the choice of chirality, which is really just our choice to use right-handed coordinates, and which goes back ...


2

Another one of these issues where careless terminology is our downfall. Indeed, on the level of the Dirac equation, such a thing as a "left-handed electron" does not exist. Every pure electron and every pure positron state is an equal mixture of left- and right-handed components. I'll call this electron (positive-frequency solution electron) the "mass basis ...



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