Reading through David Tong lecture notes on QFT.
On pages 94, he shows the action of parity on spinors. See below link:
In (4.75) he confirms that parity exchanges right handed and left handed spinors for an arbitrary representation of the Clifford algebra. But this is unclear to me.
To prove he says:
Under parity, rotations don't change sign. But boosts do flip sign.
Again this isn't clear. We are talking about a discrete Lorentz transformation, i.e. parity, which is neither a rotation nor a boost. But why we are mixing them up?