Two-loop QED with External Magnetic Field

TL;DR

This paper computes the two-loop effective Lagrangian in QED with a magnetic field and chemical potential, revealing significant contributions to magnetization and fermion density at high chemical potentials.

Contribution

It extends the understanding of QED in magnetic fields by including two-loop effects at finite chemical potential, which were previously less explored.

Findings

Two-loop effects significantly impact magnetization at high chemical potentials.

Fermion density shows notable deviations due to two-loop contributions.

De Haas-van Alphen oscillations are analyzed in this context.

Abstract

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.