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

TL;DR

This paper introduces a method combining point-splitting and generalized gauge transformations to regularize Abelian Phi^4-type Lagrangians, with applications to models including the Abelian Higgs model.

Contribution

It develops a novel regularization approach for Abelian Phi^4 Lagrangians using point-splitting and gauge transformations, applicable to various models.

Findings

Regularized Phi^4 Lagrangians with point-splitting and gauge transformations.

Application to models like the Abelian Higgs model with spontaneous symmetry breaking.

Analysis of the regularity and non-locality of the resulting action.

Abstract

Abelian Lagrangians containing Phi^4-type vertices are regularized by means of a suitable point-splitting scheme combined with generalized gauge transformations.. The calculation is developed in details for a general Lagrangean, whose fields (gauge and matter ones) satisfy usual conditions. We illustrate our results by considering some special cases, such as the ($\overline{\psi}\psi)^2 and a modified version of the Avddev-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''.