  Abelian Lagrangians containing $\lambda\phi^{4}$-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 $(\bar{\psi}\psi)^{2}$ 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''.
