Fermion and photon gap-equations in Minkowski space within the Nakanishi integral representation method

Abstract The approach based on the Nakanishi integral representation of n-leg transition amplitudes is extended to treatment self-energies a fermion and an (IR-regulated) vector boson, in order pave way for constructing comprehensive application technique both gap- Bethe-Salpeter equations, Minkowski space. achieved result, namely 6-channel coupled system eventually allows one determine three Källén–Lehman weights fully dressing propagators photon. A first consistency check also provided. presented formal elaboration points embed characteristics non-perturbative regime at more fundamental level. It yields viable tool space phenomenological investigation strongly interacting theories, within QFT framework where dynamical ingredients are made transparent under control.