A new method for calculating the covariant derivative expansions is presented, particularly in Abelian gauge theories, which can be used to find derivative expansions around nonvanishing gauge field-strength tensors. We apply this method to find the $O\left({\left({\partial }_{\lambda }{F}_{\mu \nu }\right)}^2\right)$ terms of electron determinants in quantum electrodynamics.

• Received 31 July 1989

DOI:https://doi.org/10.1103/PhysRevD.40.4202