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Help me to understand the QCD vertex factor

  1. Jun 27, 2015 #1
    Guys.....help me out to understand this 3-vertex factor of non-abelian and or QCD fields.
    it is from peskin & schroeder page 507.
     
  2. jcsd
  3. Jun 27, 2015 #2

    vanhees71

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    What specifically don't you understand?
     
  4. Jun 27, 2015 #3
    i am latexing the 2 equations in a minute that i need help for.
     
  5. Jun 27, 2015 #4
    Guys.....help me out to understand this 3-vertex factor of non-abelian and or QCD fields
    and then the 4-vertex of the same fields, it is from peskin & schroeder page 507.

    I want to understand how to get the following vertex factors.
    The equation are as follows;


    \begin{equation}

    eq-1=gf^{abc}[g^{\mu\nu}(k-p)^{\rho}+g^{\nu\rho}(p-q)^{\mu}+g^{\rho\mu}(q-k)^{\nu}]

    \end{equation}

    \begin{equation}

    eq-2=-ig^{2}[f^{abc}f^{cde}(g^{\mu\nu}g^{\nu\sigma}-g^{\mu\sigma}g^{\nu\rho})+f^{ace}f^{bde}(g^{\mu\nu}g^{\rho\sigma}-g^{\mu\sigma}g^{\nu\rho})+f^{ade}f^{bce}(g^{\mu\nu}g^{\rho\sigma}-g^{\mu\rho}g^{\nu\sigma})]

    \end{equation}
     
  6. Jun 27, 2015 #5

    Orodruin

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    You should be able to derive these interaction terms by expanding the Lagrangian density in the fields as usual.
     
  7. Jun 27, 2015 #6
    yes, I expanded just the lagrangian propotional to 1/4tr(G)^2 and got the 3 and 4 vertex terms. what I am confused is that
    how do I get these terms by permutation of what? the group indices a,b,c,?

    Bailin and Love says on page 127 that permutation of momentum and lorentz indices will give these vertex factors
    but I am having problem in computing it.
     
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