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Gamma 5 dirac matrice

  1. Jun 9, 2010 #1
    Hi, i wonder somethin'

    when I see that definition of the matrice:
    [tex]\gamma^5=\gamma^0\gamma^1\gamma^2\gamma^3[/tex]
    I don't see why it is a pseudo-scalar.
     
  2. jcsd
  3. Jun 9, 2010 #2
    If you inspect [tex]\gamma^5[/tex],you can see that it anti commutes with [tex]\gamma^0[/tex] (while 0 stands for the time coordinate).
    so under space inversion the expression will change it's sign
    [tex]\psi^{\dag}\gamma^{0}\gamma^5\psi\rightarrow-\psi^{\dag}\gamma^0\gamma^5\psi[/tex]
    and that is a property of a Pseudoscalar
     
    Last edited: Jun 9, 2010
  4. Jun 11, 2010 #3
    Hum i see, thanks :).
     
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