Derivative expansion of the effective action for quantum electrodynamics in 2+1 and 3+1 dimensions

The derivative expansion of the one-loop effective action in QED(3) and QED (4) (quantum electrodynamics) is considered. The first term in such an expa nsion is the effective action for a constant electromagnetic field. An expl icit expression for the next term containing two derivatives of the field s trength F-mu nu, but exact in the magnitude of the field strength, is obtai ned. The general results for both fermion and scalar electrodynamics are pr esented. The cases of pure electric and pure magnetic external fields are c onsidered in detail. The Feynman technique for the perturbative expansion o f the one-loop effective action in the number of derivatives is developed. (C) 1999 American Institute of Physics. [S0022-2488(99)00711-2].