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We derive the gauge covariance requirement imposed on the QED fermion-photonthree-point function within the framework of a spectral representation forfermion propagators. When satisfied, such requirement ensures solutions to thefermion propagator Schwinger-Dyson equation (SDE) in any covariant gauge witharbitrary numbers of spacetime dimensions to be consistent with theLandau-Khalatnikov-Fradkin transformation (LKFT). The general result has beenverified by the special cases of three and four dimensions. Additionally, wepresent the condition that ensures the vacuum polarization is independent ofthe gauge parameter. As an illustration, we show how the Gauge Techniquedimensionally regularized in 4D does not satisfy the covariance requirement.

How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex