# A How parity exchanges right handed and left handed spinors

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1. Dec 3, 2016

### victorvmotti

Reading through David Tong lecture notes on QFT.

On pages 94, he shows the action of parity on spinors. See below link:

[1]: http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf

In (4.75) he confirms that parity exchanges right handed and left handed spinors.

Or for an arbitrary representation of the Clifford algebra:

$$P: \psi_{+} \to \psi_{-}$$

Where

$$\psi_{+}$$ and $$\psi_{-}$$ are projections of the Dirac spinor $$\psi$$

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, on spacetime which is neither a rotation nor a boost. But why we are mixing them up? I mean a rotation and boost on the Dirac spinor?

2. Dec 8, 2016