Local gauge invariance of nonlocal interactions

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Abstract
The implication of invariance under local gauge transformation is investigated for electromagnetic interactions of nucleons and pions, which are particles extended in space time. It is shown that it is possible to derive electromagnetic interactions that are nonlocal and at the same time maintain local gauge invariance. Unlike the line current distribution assumed in the literature, the obtained current has a more flexible form that allows phenomenological analyses. It is proven that the current operators satisfy Ward-Takahashi equations for the nucleon, pion, and pion-nucleon vertex.