We evaluate the exact (2+1)-dimensional QED effective energy for charged spin-0 and spin-1/2 fields in the presence of a family of static magnetic field profiles localized in a strip of width λ. The exact result yields an infinite set of relations between the terms in the derivative expansion of the effective energy for a general magnetic field. Upon addition of the standard Maxwell magnetostatic energy, the minimum energy configuration at fixed flux corresponds to a uniform magnetic field.

• Received 13 June 1995

DOI:https://doi.org/10.1103/PhysRevD.52.R3163