Two-loop QED with External Magnetic Field

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In 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 corrected

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