There are many formally equivalent perturbative approaches to QED bound states (atoms), because even a first approximation has a non-polynomial wave function. Requiring that the gauge field be classical at lowest order selects the \hbar expansion with a stationary action. This principle allows to derive the Schrödinger equation from QED. Higher order corrections are defined as in the Interaction Picture, but with the in- and out-states being eigenstates of the Hamiltonian that includes the classical field.

Features of hadron data indicate that the \hbar expansion is relevant also for QCD bound states. The QCD scale can arise from a homogeneous, O(\alpha_s^0) solution of the field equations. Given basic physical requirements the solution appears to be unique (up to the scale). It implies a linear potential for mesons and a related confining potential for baryons. At lowest order in 1/N_c mesons lie on linear Regge trajectories and their daughters.

There are massless (M=0) states which allow an explicit realization of spontaneous chiral symmetry breaking, through mixing of the 0^{++} sigma state with the perturbative vacuum. Chiral transformations of the sigma condensate generate massless 0^{-+} pions. For a small quark mass m the pion gets a mass M \propto \sqrt{m}. The pion is annihilated by the axial vector current as expected for a Goldstone boson.