Generalized Gauge Transformations and Regularized $\lambda\phi^{4}$-type Abelian Vertices

TL;DR

This paper introduces a regularization method for Abelian Lagrangians with $$-type vertices using point-splitting and generalized gauge transformations, with applications to various models including the Abelian Higgs model.

Contribution

It develops a detailed regularization scheme for Abelian Lagrangians with $$-type vertices using point-splitting and generalized gauge transformations, applicable to multiple models.

Findings

Regularized Abelian Lagrangians with point-splitting.

Application to models like $(\bar{\psi}\psi)^2$ and Avdeev-Chizhov.

Discussion of regularity and non-locality of the regularized action.

Abstract

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''.