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