Help me to understand the QCD vertex factor

[moss]

Guys...help me out to understand this 3-vertex factor of non-abelian and or QCD fields.
it is from peskin & schroeder page 507.

 

[vanhees71]

What specifically don't you understand?

 

[moss]

What specifically don't you understand?

i am latexing the 2 equations in a minute that i need help for.

 

[moss]

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}

 

[Orodruin]

You should be able to derive these interaction terms by expanding the Lagrangian density in the fields as usual.

 

[moss]

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.