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Advice for gluon vertex textbook

  1. Nov 21, 2014 #1
    Hello everyone,
    i'm having a hard time trying to derive the three gluon vertex in QCD, using the generating functional. Could someone please suggest a reference where it is computed step by step? My teacher lecture notes are not clear, and basically I don't understand what he's doing.
    A very good reference on Green functions could be useful as well.
    Thanks a lot!
  2. jcsd
  3. Nov 21, 2014 #2
    I'd check out chapt. 9 of Cheng & Li -- Gauge Theory of Elementary Particles, where everything is derived using path integrals.
  4. Nov 21, 2014 #3


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    I have the calculation in my notes, which have text in Romanian. I don't think you have the explicit hand-made calculations in any book (my notes are built upon the brilliant book by Bailin & Love). You shouldn't look for a book to show the calculation, you can do it by yourself:

    You read off the 3 vertex gluon factor once you put the 3-field term in the Lagrangian action from x to p representation with 4D Fourier transform. The 3-field expansion of int d^4 x F_a^{mu nu} F^{a}_{mu nu} you should calculate by yourself (it's gAApartialA), then trans-Fourier the product of 3 fields, then use the symmetry property (3 bosons).

    Since this the is the book recommendation section, you can warmly use D.Bailin's and A.Love's "Introduction to Gauge Field Theory", IOP, 1993 for any QFT/Green functions questions.
  5. Nov 22, 2014 #4


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    A good standard text on QCD is Muta, Quantum Chromodynamics.
  6. Nov 23, 2014 #5
    Thank you for your kind answers :)
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