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 snooper007 Jun4-06 10:45 PM

help! About charge conjugation of Dirac spinor

The following formula appears in P J Mulders's lecture notes
http://www.nat.vu.nl/~mulders/QFT-0E.pdf

$${\cal C}~b(k,\lambda)~{\cal C}^{-1}~=~d(k,{\bar \lambda})$$ (8.18)

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

Thanks

 reilly Jun8-06 02:04 PM

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.
Regards,
Reilly Atkinson

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