Abstract
The thermal averaged real-time propagator of a Dirac fermion in a static uniform magnetic field B is derived. At nonzero chemical potential and temperature we find explicitly the effective action for the magnetic field, which is shown to be closely related to the Helmholtz free energy of a relativistic fermion gas, and it exhibits the expected de Haas-van Alphen oscillations. An effective QED coupling constant at finite temperature and density is derived, and compared with renormalization group results. We discuss some astrophysical implications of our results.
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