In Yang-Mills theories (and more complicated theories with additional matter fields) we have three and four gauge boson vertices, boson-ghost and boson-matter vertices. Perturbative divergences present in all of them are perfectly correlated - once divergences in propagators are removed by rescaling of fields and massess, we can absorb all divergences in vertices by a redefinition of single coupling constant. This makes me wonder whether some relations hold also between finite parts of vertices.
- I am aware of the spinor-helicity machinery. As far as I understand this applies mostly to scattering amplitudes of on-shell gluons. My question is about something more general, namely arbitrary correlation functions $\langle A(x_1)...A(x_n) \rangle $ in some gauge.
- I know about Slavnov-Taylor identities, BRST invariance and all that. However I have no idea how to use this machinery to look for relations between $\langle AAA \rangle$ and $\langle AAAA \rangle$ or $\langle \bar c c A \rangle$. I have some partial results involving these three vertices, but unfortunately it involves also higher vertices $\langle \bar c c A A \rangle$.