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Abstract
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 $O({({\ensuremath{\partial}}_{\ensuremath{\lambda}}{F}_{\ensuremath{\mu}\ensuremath{\nu}})}^{2})$ terms of electron determinants in quantum electrodynamics.
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