Feynman rules for vector bosons

  • Thread starter wangjiaji
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  • #1
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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.
 

Answers and Replies

  • #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:
 
  • #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.
 
  • #4
Avodyne
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Try Srednicki's book. A draft copy is available free at his web page.
 

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