Fermion and Photon gap-equations in Minkowski space within the Nakanishi Integral Representation method

Understand

The approach based on the Nakanishi integral representation of n-leg transition amplitudes is extended to the treatment of the self-energies of a fermion and an (IR-regulated) vector boson, in order to pave the way for constructing a comprehensive application of the technique to both gap- and Bethe-Salpeter equations, in Minkowski space.

• The achieved result, namely a 6-channel coupled system of integral equations, eventually allows one to determine the three K\"all\'en-Lehman weights for fully dressing the propagators of fermion and photon.
• A first consistency check is also provided.
• The presented formal elaboration points to embed the characteristics of the non-perturbative regime at a more fundamental level.