Construction of gauge invariant effective nucleonic theories: functional approach
Starting from relativistic quantum field theories, describing interacting nucleons and pions coupled to the dynamical electromagnetic field, the pion degrees of freedom are eliminated by means of functional integration. Apart from taking into account some operators perturbatively in $e$, e.g. the vacuum polarization, this procedure is exact, giving effective theories for nucleons and photons. The subsequent nonrelativistic reduction yields the corresponding nonrelativistic quantum field theory. The latter is unique, irrespective of the precize form of the original nucleon-pion interaction. Nucleonic potentials and electromagnetic interactions are mutually consistent. Local gauge invariance is satisfied at any stage of the formal developments.