Temperature expansions for magnetic systems

We derive finite temperature expansions for relativistic fermion systems in the presence of background magnetic fields, and with nonzero chemical potential. We use the imaginary-time formalism for the finite temperature effects, the proper-time method for the background field effects, 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 temperature limit, but we also discuss the T = 0 limit with nonzero chemical potential. (C) 1996 Academic Press, Inc.