Reading through David Tong lecture notes on QFT.

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

QFT notes by Tong

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?

  • $\begingroup$ This is e.g. explained in footnote 3 of my Phys.SE answer here. $\endgroup$ – Qmechanic Nov 17 '16 at 16:34
  • $\begingroup$ In physical terms this is because chirally dual spinors (right and left handed) are the spin-orthogonal, space inverted of each other. For details see also physics.stackexchange.com/q/263047 . $\endgroup$ – udrv Nov 18 '16 at 16:04

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