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

• Osiris
In summary, the conversation discusses a mistake found in the derivation of EQ. (15.7.19) on page 30 of the book "Quantum Field Theory" regarding the nilpotency of the BRST operator on the ghost for gauge transformation. It is pointed out that a plus sign should be a minus sign in order for the BRST operator to be nilpotent on the ghost.
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.

Last edited by a moderator:
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.

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.

## 1. What is the mistake in Steven Weiberg's QFT II textbook?

There is no known mistake in Steven Weiberg's QFT II textbook. However, as with any scientific text, there may be minor errors or typos that are corrected in subsequent editions.

## 2. How reliable is Steven Weiberg's QFT II textbook?

Steven Weiberg's QFT II textbook is considered to be a highly reliable source for quantum field theory, as Weiberg is a respected physicist and the book has been cited and used by many other scientists in their research.

## 3. Can I trust the information in Steven Weiberg's QFT II textbook?

Yes, the information in Steven Weiberg's QFT II textbook is generally accepted as accurate and trustworthy by the scientific community. However, it is always important to critically evaluate any information and consult multiple sources.

## 4. Are there any known errors in Steven Weiberg's QFT II textbook?

As mentioned before, there are no known major errors in Steven Weiberg's QFT II textbook. However, it is always possible that there may be minor errors or typos that have been corrected in subsequent editions.

## 5. How can I report a potential mistake in Steven Weiberg's QFT II textbook?

If you believe you have found a mistake in Steven Weiberg's QFT II textbook, you can contact the publisher or the author directly to report it. It is important to provide specific details and evidence to support your claim.

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