Electromagnetic fields in a thermal background

The one-loop effective action for a slowly varying electromagnetic field is computed at finite temperature and density using a real-time formalism. Some earlier errors in the literature are corrected. The effective coupling constant, defined from a purely electric weak-field expansion, behaves at high temperature very differently from the case of a magnetic field, and does not satisfy the renormalization group equation. No thermal corrections to pair production are found at the one-loop level in this formalism.