Momentum-cutoff regularization and gauge invariance in QED

Based on a gauge-invariant form of the electron propagation function, we propose a formalism for QED which preserves its gauge-invariant character when both photon and electron propagators are regularized with a sharp momentum-cutoff procedure. Perturbation calculations of the regularized fermion effective action functional of an external electromagnetic field are given. We study radiative corrections induced by a momentum-cutoff vacuum and derive the corresponding Ward–Takahashi identity. Several problems encountered in an attempt of constructing a momentum-cutoff QED model are discussed.