Interparticle potential energy for D-dimensional electromagnetic models from the corresponding scalar ones

TL;DR

This paper introduces a method to derive interparticle potentials in D-dimensional electromagnetic models from scalar models using a correspondence principle, analyzing their behavior and ghost presence.

Contribution

It presents a novel approach linking electromagnetic and scalar potentials in D-dimensions, simplifying calculations for higher-derivative models and clarifying ghost issues.

Findings

Derived electromagnetic potentials from scalar counterparts in D-dimensions.

Analyzed potential behavior at large and small distances.

Investigated ghost presence and Coulomb singularity absence.

Abstract

Using a method based on the generating functional plus a kind of "correspondence principle" --- which acts as a bridge between the electromagnetic and scalar fields --- it is shown that the interparticle potential energy concerning a given $D$-dimensional electromagnetic model can be obtained in a simple way from that related to the corresponding scalar system. The $D$-dimensional electromagnetic potential for a general model containing higher derivatives is then found from the corresponding scalar one and the behavior of the former is analyzed at large as well as small distances. In addition, we investigate the presence of ghosts in the four-dimensional version of the potential associated with the model above and analyze the reason why the Coulomb singularity is absent from this system. The no-go theorem by Ostrogradski is demystified as well.