Dynamical Perturbation Theory and the Auxiliary Field Method

By introducing auxiliary fields, which by their quantum numbers vanish in perturbation theory, we relate the dynamical perturbation theory of Pagels and Stokar and a successful gauged nonlocal constituent quark model to $U(N)$ gauge theory and to QCD. This sheds light on the duality between quark models and resonance models. We then derive the effective action in the loop expansion without dropping cubic and quartic gluon couplings.