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One stupid question about Weinberg's Volume 1

  1. Dec 22, 2009 #1
    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 any one explain it for me?

    Thanks
     
  2. jcsd
  3. Dec 22, 2009 #2
    [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.
     
  4. Dec 22, 2009 #3
    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.
     
  5. Dec 22, 2009 #4
    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.
     
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