Effective Fermion Mass in Relativistic and Non-Relativistic Systems

Electrons interact strongly with their environment. The result of these interactions is, most of the time, encoded in an effective mass. In non-relativistic systems, as in condensed matter, the electrons plus interactions form a quasiparticle with an effective mass. From the side of relativistic systems, the fermions also acquire an effective mass due to the interactions with the surrounding medium. We employ a non-perturbative method to calculate the effective mass of relativistic and non-relativistic fermions, in various situations. We find the effective masses up to second order of the iteration method. The results can be of interest in current studies on fermion systems.