Magnetars and heavy-ion-collisions (HIC) are environments where only a robust theory of strong interactions can extract reasonable quantities according to the recent astronomical observations and HIC-experiments. Because of the sign problem, the Lattice Quantum Chromodynamics (LQCD) isn’t treatable in important cases where there are finite chemical potentials. The Nambu–Jona-Lasinio (NJL) model, one of the most prominent among the effective models for QCD, allowed a lot of questions in low energy hadron physics to be studied. The thermodynamic properties of the QCD phase diagram can be altered in a non-negligible way under an electromagnetic field and taking a phenomenological term of anomalous magnetic moment (AMM). Here, we will present the general Quantum Electrodynamics (QED) formalism which this work is based and so we will obtain the Green function associated with the NJL--SU(2) density lagrangian.