Primitively divergent diagrams in $\kappa$-deformed scalar field with quartic self-interaction

TL;DR

This paper investigates how $ppa$-deformation affects divergent diagrams in a four-dimensional scalar field theory with quartic interaction, revealing finite results due to deformation-induced pole displacement.

Contribution

It provides the first analysis of primitively divergent diagrams in $ppa$-deformed scalar fields, showing deformation leads to finite regularized results.

Findings

Deformation causes a displacement of poles in complex plane.

Dimensional regularization yields finite results at four dimensions.

Fundamental length scale influences divergence structure.

Abstract

We obtain the primitively divergent diagrams in $\kappa$-deformed scalar field in four-dimensional spacetime with quartic self-interaction in order to investigate the effect of the fundamental length $q=1/(2\kappa)$ on such diagrams. Thanks to $\kappa$-deformation, we find that the dimensionally regularized forms of the diagrams lead to finite results in the limit of space-time dimension four. The effect of the deformation appears as a displacement of the poles in the complex plane.