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A How parity exchanges right handed and left handed spinors

  1. Dec 3, 2016 #1
    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:

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


    $$ \psi_{+}$$ 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. jcsd
  3. Dec 8, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
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