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Γ5 and chiral symmetry

  1. Sep 5, 2010 #1
    recently i am reading chiral symmetry in QFT. Almost all textbooks define γ5 as a chiral
    operator without saying some reasons. i am very confused why γ5 has something to do with
    chiral symmetry, can somebody explain it more intuitively and physically? who first introduce γ5 as a chiral operator? and i also want to
    know what is a chiral transformation? is it a transformation for example which can transform a left-handed to a right-handed?

  2. jcsd
  3. Sep 6, 2010 #2


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    The states projected out by the projectors [tex] (1 \pm \gamma_5)/2 [/tex] can be seen to be interconverted into each other by the parity operator [tex] i \gamma_0 [/tex] as it anticommutes with gamma_5. On the other hand time reversal as given by [tex] i\gamma_1\gamma_3 [/tex] and taking the complex leaves these states invariant. Compare this to the properties of a chiral molecule under parity and time-reversal: under parity (space inversion), a D molecule will be transformed into an L molecule and vice versa, while time inversion leaves the chirality of the molecule the same.
    The chirality transformation corresponds to a multiplication of these two components by phase factors [tex] \exp (\pm i \phi) [/tex].
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