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1PI Green functions 3-gluon vertex amplitudes anticommute antisymmetric appendix bosonic classical equations collective index color factor color weight combinatoric combinatoric factors Compton scattering Compute connected Green functions covariant gauges decouple defined degrees of freedom derivatives DS equations dW[J Dyson-Schwinger equations effective action Euclidean example Exercise extra term fermionic generating functionals fermionic Green functions Feynman diagrams Feynman rules formalism free field theory full Green functions gauge fixing gauge invariance gaugeon insertion Gaussian integral Ghoulies gluon gluon propagator hermitian hermitian matrix Hint hopping probability interactions inverse Jacobi identities Lie algebra long-leggety beasties loop expansion mass-shell matrix Minkowski indices NORDITA one-loop path integral Pauli principle perturbation expansion photon physical polarization propagators and vertices QED-like quantum mechanics quark Quefithe relation renormalization replaced rewrite S-matrix scalar self-energy Show sources spacetime spin SU(n supersymmetry symmetry three-gluon vertex tion transformation transverse vacuum bubbles vanish vertex Ward identity Ward identity 6.37