2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51056Abelian Lagrangians containing $λϕ^{4}$-type vertices are regularized by means of a suitable point-splitting scheme combined with generalized gauge transformations. The calculation is developped in details for a general Lagrangian whose fields (gauge and matter ones) satisfy usual conditions. We illustrate our results by considering some special cases, such as the $(\barψψ)^{2}$ and the Avdeev-Chizhov models. Possible application of our results to the Abelian Higgs model, whenever spontaneous symmetry breaking is considered, is also discussed. We also pay attention to a number of features of the point-split action such as the regularity and non-locality of its new ``interacting terms''.11 pages, no figures. Latex format. Submitted to New Journal PhysicsHigh Energy Physics - Theorytext