Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help! About charge conjugation of Dirac spinor

  1. Jun 4, 2006 #1
    The following formula appears in P J Mulders's lecture notes
    http://www.nat.vu.nl/~mulders/QFT-0E.pdf [Broken]

    [tex]{\cal C}~b(k,\lambda)~{\cal C}^{-1}~=~d(k,{\bar \lambda})[/tex] (8.18)

    where [tex]{\cal C}[/tex] is charge conjugation operator.
    [tex]\lambda[/tex] is helicity.
    I don't know why there is [tex]{\bar {\lambda}}[/tex] on the right side,
    as is well known that charge conjugation can not change helicity, spin, and momentum.

    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Jun 8, 2006 #2


    User Avatar
    Science Advisor

    The phases used to define negative energy or anti-particle spinors are often author dependent -- for example, the C matrix is diagonal in Weinberg's book, and off diagonal in Gross's text. Gross uses a different convention for defining antiparticle spinors than do Bjorken and Drell As far as I can figure, you'll have to track through the charge-c process starting with Mulder's conventions for particle and antiparticle spinors. Note that often the CCD relates the complex conjugate antiparticle spinor to the particle spinor. Good luck.
    Reilly Atkinson
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook