So as I understand it, under a parity transformation $\psi(x,t) \rightarrow \gamma^{0}\psi(-x,t)$. This to me then is not an eigenspinor of the parity operator - so how do we assign it a definite parity?
I was reading Griffiths' Introduction to Elementary Particles, and question 4.35 asks
Is the neutrino an eigenstate of parity? If so, what is its intrinsic parity?
The solution manual says that the answer is "No, because a parity transformation would convert a left handed neutrino into a right handed one (in the massless limit) which does not even exist".
I can kind of see the reasoning as being, "the neutrino possesses no right handed counterpart, and so cannot be put into a Dirac spinor which could be a pairity eigenstate", but this still doesn't answer my general question about assigning parity, and I'm not sure my reasoning for the neutrinos is right either.
