Effective Fermion Mass in Relativistic and Non-Relativistic Systems

TL;DR

This paper presents a non-perturbative method to calculate the effective mass of fermions in both relativistic and non-relativistic systems, providing insights into how interactions influence fermion properties across different regimes.

Contribution

It introduces a non-perturbative iterative approach to compute fermion effective masses in diverse physical contexts, extending beyond traditional perturbative techniques.

Findings

Effective masses calculated up to second order.

Method applicable to various relativistic and non-relativistic systems.

Results relevant for current fermion system studies.

Abstract

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.