  Using the exact propagators in a constant magnetic field, the effective
electromagnetic Lagrangian at finite temperature and density is calculated to
all orders in the field strength B within the framework of the complete
electroweak model, in the weak coupling limit. The partition function and free
energy are obtained explicitly and the finite temperature effective coupling is
derived in closed form. Some implications of this result, potentially
interesting to astrophysics and cosmology, are discussed.
