Is this a mistake in Steven Weiberg's QFT II textbook?

1. Dec 24, 2009

Osiris

I guess it should be my mistake somewhere.
https://www.amazon.com/Quantum-Theory-Fields-Modern-Applications/dp/0521670543/ref=pd_bxgy_b_text_b

On Page 30, for the derivation of EQ. (15.7.19), the nilpotency of BRST operator on the ghost for gauge transformation,

$$\delta _{\theta}s\omega_\alpha &=& - \frac{1}{2}C_{\alpha\beta\gamma}\delta_\theta(\omega_\beta\omega_\gamma) &=&\frac{1}{4}\theta (C_{\alpha\beta\gamma}C_{\beta\delta\epsilon}\omega_\delta\omega_\epsilon\omega_\gamma ++ C_{\alpha\beta\gamma}C_{\gamma\delta\epsilon}\omega_\beta\omega_\delta\omega_\epsilon)=...$$

The plus "++" above, I suppose it should be "-" considering $$\omega$$ is an anticommuting ghost and the BRST operator is odd and acting from left. Steven also mentioned this in the paragraph below Eq. (15.7.19).

Did I miss any point here? Since then we would not have nilpotency of BRST operator on the ghost.

Last edited by a moderator: Apr 24, 2017