We derive finite temperature expansions for relativistic fermion syste
ms in the presence of background magnetic fields, and with nonzero che
mical potential. We use the imaginary-time formalism for the finite te
mperature effects, the proper-time method for the background field eff
ects, and zeta function regularization for developing the expansions.
We emphasize the essential difference between even and odd dimensions,
focusing on 2 + 1 and 3 + 1 dimensions. We concentrate on the high te
mperature limit, but we also discuss the T = 0 limit with nonzero chem
ical potential. (C) 1996 Academic Press, Inc.