Point-Splitting as a Regularisation Method for <math>λϕ4</math> -Type Vertices: Abelian Case

Physics NotePublished

Point-Splitting as a Regularisation Method for $<math>\lambda\varphi^{4}</math>$ -Type Vertices: Abelian Case

W. A. M. Melo; José Abdalla Helayel Neto

1998

Authors: W. A. M. Melo; José Abdalla Helayel Neto
Type: Physics Note
Status: Published
Publication date: 1998
Description: We obtained regularised Abelian Lagrangeans containing <math>\lambda\varphi^{4}\,\!</math> -type vertices by means of a suitable point-splitting procedure. The calculation is developed in details for a general Lagrangean, whose fields (gauge and matter ones) satisfy certain conditions. We illustrate our results by considering some special cases, such as the Abelian Higgs, the <math>(\overline{\psi}\psi)^{2}\,\!</math> and the Avdeev-Chizov (real and rank-2 antisymmetric tensor as matter fields) models. We also discuss some features of the obtained Lagrangean such as the regularity and non-locality of its new interacting terms. Moreover, the resolution of the Abelian case may teach us some useful technical aspects when dealing with the non-Abelian one.
Year: 1998
Number: CBPF-NF-061/98
Linked to a thesis: No
Linked to a grant: No