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Feynman rules for vector bosons

  1. Jan 18, 2009 #1
    I'm learning QFT by reading Lewis Ryder's book, so my question in short is: how he arrives at Eq 7.57 and Eq 7.58? If you don't have the book, the question is: why are there Minkowski metric terms in the Feynman rules for a gauge field coupling to itself? If the answer is complicated, simply tell me where I can find it please, I have Peskin's and Weinberg's book, too.

    For me it seems impossible to proceed after Chapter 7 with this book, it doesn't have a systematic way of introducing Feynman diagrams, and the Feynman rules for vector bosons seem to be pulled out of a hat, is this a suitable book for a man learning QFT for the first time on his own?

    Thank you.
     
  2. jcsd
  3. Jan 23, 2009 #2

    tiny-tim

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    in Weinberg?

    Hi wangjiaji! :smile:

    I don't have Ryder's book, but I do have Weinberg's Quantum Theory of Fields Volume I …

    which page number, and which equations, is it in Weinberg? :smile:
     
  4. Jan 26, 2009 #3
    To derive the precise form of the Feynman rule, it would be best for you to work it out starting from the LSZ reduction formula for the scattering processes [itex]gg\rightarrow g[/itex] and [itex]gg\rightarrow gg[/itex]. Essentially, the Minkowski metric arises from needing to expand the 4-vector dot products between the vector fields in the interacting Lagrangian before proceeding to contract fields:
    [tex]A_\mu A^\mu=g_{\mu\nu}A^\mu A^\nu[/tex]​

    Physically speaking, the role of the Minkowski metric in the Feynman rules for the 3- and 4- vector boson vertices is to select, depending on the polarization of the incoming and outgoing vector bosons, the appropriate Clebsch-Gordon coefficient arising from the coupling of two spin-1 systems.
     
  5. Jan 26, 2009 #4

    Avodyne

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    Try Srednicki's book. A draft copy is available free at his web page.
     
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