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

[Osiris]

I guess it should be my mistake somewhere.
https://www.amazon.com/dp/0521670543/?tag=pfamazon01-20

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.

 

[Adrmay]

Yes, you are correct. The plus sign should be a minus sign, as you said. Without the correct minus sign, the BRST operator would not be nilpotent on the ghost and the derivation of EQ. (15.7.19) would not be correct.

 

[charng]

it is important to thoroughly review and analyze any potential mistakes or discrepancies in scientific literature. In this case, it does appear that there may be a mistake in the derivation of EQ. (15.7.19) in Steven Weiberg's QFT II textbook. The use of a plus sign instead of a minus sign does appear to contradict the fact that \omega is an anticommuting ghost and the BRST operator is odd. It is also important to note that this mistake was acknowledged by the author in the paragraph below the equation. This may have been a simple oversight or typo, but it is important to address and correct in order to maintain the accuracy and validity of the text. I would recommend reaching out to the author or publisher to clarify and potentially correct this mistake for future editions. In the meantime, it would be beneficial to double check any calculations or derivations using this equation to ensure the correct result is obtained.