2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149246In two - loop effective Lagrangian, the low - temperature expansion of the $QED_{3+1}$ with a constant magnetic field and a finite chemical potential is performed. We then calculate the total fermion density, some components of polarization operator and de Hass -van Alphen oscillations. We find that there is a significant contribution from two-loop expansion to magnetization and fermion density for higher values of chemical potentials.12 pages (LaTex) and 5 postscript figures added. Replaced to remove blocks of text accidentally copied verbatim from papers by V. Zeitlin (hep-ph/9412204 and hep-ph/9507404) and some typos are correctedHigh Energy Physics - Theorytext