In reading Ryder's book on quantum field theory he advocates reading off the Feynman rules directly from the Lagrangian in the path integral quantization method. I can sort of do this in phi-four theory, but it is not obvious in for example Yang-Mills theory, so I wondered if someone could explain to me why it is obvious that for example the term(adsbygoogle = window.adsbygoogle || []).push({});

##2gf^{abc}A^b_\mu A^c_\nu(\partial^\mu A^{\nu a}-\partial^\nu A^{\mu a})##

corresponds to

##-2gf^{abc}[(r_\mu -q_\mu)g_{\nu \rho}-(p_\nu -r_\nu)g_{\mu \rho} + (q_\rho - p_\rho)g_{\mu \nu}].##

where r,p and q are the momenta of the gauge bosons while a,b,c are their group indicies.

I see that the derivatives goes over to momenta in momentum space, but what is the origin of the 'antisymmetry' between the momenta?

How does one 'see' the exact structure?

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# Feynman rules from Yang-Mills lagrangian

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