Feynman rules for vector bosons

[wangjiaji]

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.

 

[tiny-tim]

in Weinberg?

Hi wangjiaji!

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?

 

[TriTertButoxy]

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 $gg\rightarrow g$ and $gg\rightarrow gg$. 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:

$$A_\mu A^\mu=g_{\mu\nu}A^\mu A^\nu$$​

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.

 

[Avodyne]

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