Help with page 73 of Weinbergs QFT, vol.1

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In summary, the conversation is discussing an error in an equation (2.5.47) and the resulting phase difference under parity and time reversal for a massless particle. It is mentioned that the issue may be related to the active rotation vs. passive rotation problem, but it is not clear. The sign in the equation is said to be inconsequential and can be changed to rotate in the other direction, and it should not affect parity. The speaker later realizes their mistake and clarifies the correct equation for rotation around the 3 axis.
  • #1
Reggaerules
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In equation (2.5.47),

I am getting
U(R(\hat p) = e^{+i \phi J_3} e^{+i \theta J_2}

Instead of the "-" signs in the exponential. This makes a phase difference under parity and time reversal of a massless particle.

Is this one of the active rotation vs. passive rotation problem? If so, it is not clear to me.

Oops, I think, the problem may be with (2.4.27)
 
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  • #2
The sign is inconsequential it just tells you which direction you are rotating clockwise or counterclockwise. If you don't like the sign rotate the other direction. It shouldn't effect parity since parity is not a rotation.
 
  • #3
It turns out that it was an error on my part. For example, for rotation by angle \phi around the 3 axis, I get

e^{-i \phi J_3} since \omega_{12} = - \phi.
 

Related to Help with page 73 of Weinbergs QFT, vol.1

1. How do I solve problems on page 73 of Weinberg's QFT, vol.1?

To solve problems on page 73 of Weinberg's QFT, vol.1, you should first carefully read the problem and understand the question being asked. Then, review any relevant concepts or equations from the textbook and try to apply them to the problem. It may also be helpful to consult with peers or a professor for assistance.

2. Can you provide step-by-step solutions for the problems on page 73 of Weinberg's QFT, vol.1?

As a scientist, I cannot provide step-by-step solutions for the problems on page 73 of Weinberg's QFT, vol.1. However, you can find detailed solutions in the back of the textbook or online resources.

3. Are there any common mistakes to avoid when solving problems on page 73 of Weinberg's QFT, vol.1?

Some common mistakes to avoid when solving problems on page 73 of Weinberg's QFT, vol.1 include not fully understanding the question, using incorrect equations or concepts, and making calculation errors. It is important to carefully read the problem and double check your work to avoid these mistakes.

4. What resources can I use for additional help with page 73 of Weinberg's QFT, vol.1?

In addition to the textbook and class materials, you can use online resources such as forums, study groups, and tutorial videos for additional help with page 73 of Weinberg's QFT, vol.1. You can also consult with your professor or attend office hours for further clarification.

5. How can I improve my understanding of the concepts on page 73 of Weinberg's QFT, vol.1?

To improve your understanding of the concepts on page 73 of Weinberg's QFT, vol.1, it is important to actively engage with the material. This can include practicing problems, discussing with peers, and seeking clarification from your professor. It may also be helpful to review related material from previous chapters or seek out additional resources for a deeper understanding.

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