Preference of Chirality I was interested to see that ,
$$
\gamma^5 \psi = \psi_R - \psi_L
$$
By the definition of chirality projection operator and that $\psi = \psi_R + \psi_L$.
since $\gamma^5 \psi$ pops up a lot in QED, I thought it was interesting that $\psi_R$ should necessarily by the positive quantity in this relation. 
Is there theorem or book that may explain why we prefer $\psi_R - \psi_L$ rather than the reverse?
 A: 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 originally to how Newton defined the polar angle in polar coordinates, is tied into all sorts of aspects of modern geometry and physics.  Since the weak interactions are (unlike everything else in physics) not invariant under parity, it actually makes a difference there (and only there) which choice was made; and it's slightly inconvenient that the $W$ field only couples to the negative chirality fermions.  However, fixing this would require undoing a lot of previous work, which would be unnecessarily confusing and not worth the small benefit of eliminating one minus sign.  (We could put an extra negative sign in $\gamma_{5}$ and go no further, but this would introduce a minus sign in the relationship between chirality and helicity, which would probably not be an improvement.  Changing the definition of helicity, in turn, would require us to go back and do everything in left-handed coordinates, changing the definition of the cross product, etc.--certainly not worth the trouble.)
