The one-particle states as well as the fields in quantum field theory are regarded as representations of Poincare group, e.g. scalar, spinor, and vector representations.
Is there any systematical procedure that one starts from the Dynkin label for a given representation, to construct a Lagrangian of that field theory? If yes, where can I find that procedure?
I don't care adding interaction by gauge invariance from these Lagrangians will cause non-renormalizability or not. I can live with effective theories.