Insignificance of the anomalous magnetic moment of charged fermions for the equation of state of a magnetized and dense medium

We investigate the effects of the anomalous magnetic moment (AMM) in the equation of state (EOS) of a system of charged fermions at finite density in the presence of a magnetic field. In the region of strong magnetic fields (eB > m(2)), the AMM is found from the one-loop fermion self-energy. In contrast to the weak-field AMM found by Schwinger, in the strong magnetic field region the AMM depends on the Landau level and decreases with it. The effects of the AMM in the EOS of a dense medium are investigated at strong and weak fields using the appropriate AMM expression for each case. In contrast with what has been reported in other works, we find that the AMM of charged fermions makes no significant contribution to the EOS at any field value.