One stupid question about Weinberg's Volume 1

In summary, the conversation discusses the disagreement with the usage of \sigma in the result of space reversal transformation in Weinberg's quantum field theory. It is clarified that \sigma is an eigenvalue of the helicity operator and changes its sign under the transformation. The confusion arises from the change in the definition of \sigma in the process.
  • #1
ap_nhp
7
0
When I read quantum field theory in Weinberg's Volume 1. In equation 2.6.22 :
[tex]P{\Psi _{p,\sigma }} = {\eta _\sigma }\exp ( \mp i\pi \sigma ){\Psi _{{\cal P}p,{-\sigma} }}[/tex]

I don't agree with the [tex]-\sigma[/tex] in the result of space reversal transformation.

Can anyone explain it for me?

Thanks
 
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  • #2
ap_nhp said:
When I read quantum field theory in Weinberg's Volume 1. In equation 2.6.22 :
[tex]P{\Psi _{p,\sigma }} = {\eta _\sigma }\exp ( \mp i\pi \sigma ){\Psi _{{\cal P}p,{-\sigma} }}[/tex]

I don't agree with the [tex]-\sigma[/tex] in the result of space reversal transformation.

Can anyone explain it for me?

Thanks

[tex]\sigma[/tex] is an eigenvalue of the helicity operator [tex](\mathbf{J} /cdot \mathbf{P})P^{-1}[/tex]. This operator changes its sign under the space reversal transformation. Therefore, [tex]\sigma[/tex] also changes its sign. Don't you agree with that?

Eugene.
 
  • #3
meopemuk said:
[tex]\sigma[/tex] is an eigenvalue of the helicity operator [tex](\mathbf{J} /cdot \mathbf{P})P^{-1}[/tex]. This operator changes its sign under the space reversal transformation. Therefore, [tex]\sigma[/tex] also changes its sign. Don't you agree with that?

Eugene.

Thank meopemuck. I 've read again. And I see that the definition of Weinberg is little bit change in the process. He used [tex]\sigma[/tex] in [tex]{\Psi _{k,\sigma }}[/tex] as eigenvalue of [tex] J_{3}[/tex] but in [tex]{\Psi _{p,\sigma }}[/tex] is helicity. That makes me confuse.
 
  • #4
meopemuk said:
[tex]\sigma[/tex] is an eigenvalue of the helicity operator [tex](\mathbf{J} /cdot \mathbf{P})P^{-1}[/tex]. This operator changes its sign under the space reversal transformation. Therefore, [tex]\sigma[/tex] also changes its sign. Don't you agree with that?

Eugene.

Thank meopemuck. I've read Weinberg again. And I see that the definition of [tex]\sigma[/tex] change in process. Before, he used it as eigenvalue of [tex]{J _ {3}}[/tex]. And then he used it as helicity. That makes me confuse. But now I understand the reason of his definition.

Thank you one more time.
 

1. What is the main focus of Weinberg's Volume 1?

The main focus of Weinberg's Volume 1 is on the foundations of quantum mechanics and its mathematical formulation. It covers topics such as wave mechanics, matrix mechanics, and the Schroedinger equation.

2. Is Weinberg's Volume 1 suitable for beginners?

No, Weinberg's Volume 1 is not suitable for beginners. It assumes a strong background in mathematics, including linear algebra and calculus, as well as a basic understanding of quantum mechanics.

3. How does Weinberg's Volume 1 compare to other textbooks on quantum mechanics?

Weinberg's Volume 1 is considered to be one of the most rigorous and comprehensive textbooks on quantum mechanics. It is often used as a reference text for graduate-level courses on the subject.

4. Can Weinberg's Volume 1 be used for self-study?

While it is possible to use Weinberg's Volume 1 for self-study, it is recommended to have a strong background in mathematics and knowledge of quantum mechanics beforehand. The text can be challenging and may require additional resources for clarification.

5. Are there any prerequisites for reading Weinberg's Volume 1?

Yes, there are several prerequisites for reading Weinberg's Volume 1. These include a strong background in mathematics, specifically linear algebra and calculus, as well as a basic understanding of quantum mechanics. It is also helpful to have some familiarity with special relativity and classical mechanics.

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