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Confusion from Weinberg's QFT

  1. Aug 26, 2012 #1
    Hello, a confusion has arose during my so far study of the above book.

    According to the composition rule (2.3.11) it should be: [itex]U\left( \Lambda ,a \right)=U\left( \mathbf{1},a \right)U\left( \Lambda \right)[/itex] and according to transformation law (2.5.3) and the eigenvalue equation which follows (2.5.1), it should be:

    [itex]U\left( \Lambda ,a \right){{\Psi }_{p,\sigma }}={{e}^{-i\left( \Lambda p \right)\cdot a}}\sum\limits_{{{\sigma }'}}{{{C}_{{\sigma }'\sigma }}\left( \Lambda ,p \right){{\Psi }_{\Lambda p,{\sigma}' }}}[/itex]​

    Right? If yes, then my question is: how are the above compatible with eq. (3.1.1), since the phase factor that appears in the beginning of the RHS of this equation, contains the untrasformed four-momentums of the particles? Shouldn’t the phase of this factor be the following:

    [itex]-i{{a}_{\mu }}\left[ {{\left( \Lambda {{p}_{1}} \right)}^{\mu }}+{{\left( \Lambda {{p}_{2}} \right)}^{\mu }}+... \right][/itex]
    ???

    Thank' s in advance for your replies
     
  2. jcsd
  3. Aug 26, 2012 #2

    Bill_K

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    Science Advisor

    Isn't that what it is? That's what it says in my book. Maybe there was a misprint that got corrected.
     
  4. Aug 27, 2012 #3
    Then obviously my print has some mistakes. Thank’ s a lot Bill_K , now I can continue my study…
     
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