C and T conjugations

[lukeburns]

If I want to use $\psi\pm$ rather than $\langle \psi \rangle\pm$, then I need to consider conjugations for Equations 17 and 19, instead of Equation 16. C and T conjugations carry an extra change in helicity ($p_0 \mapsto \bar{p_0}$), so it's incorrect to say that Equations 17 and 19 have charge and time conjugations. They simply do not exist.

On the other hand, what ultimately matters is how observables change. While $p_0$ maps to $\bar p_0$, $J = \psi p_0 \widetilde \psi$ simply maps to $-J$, the helicity of which is unchanged. This would suggest that this works out fine.

[lukeburns]

Revert to https://github.com/lukeburns/dirac/blob/e07789485fff638f9d6fcb2de7fb5a5963ab4480/dirac.pdf?

[lukeburns]

• [ ] Discuss the effects of conjugations on observables