Simple prescription for computing the nonrelativistic interparticle potential energy related to dual models

TL;DR

This paper generalizes a method for computing nonrelativistic interparticle potentials to include dual models, analyzing various spin-0 and spin-1 mediated interactions with different field descriptions.

Contribution

It extends a previous prescription to encompass dual models and analyzes interactions mediated by various tensor and vector fields, including higher-derivative cases.

Findings

Generalized the potential energy computation to dual models.

Analyzed interactions mediated by spin-0 and spin-1 particles.

Included higher-derivative and tensor field models.

Abstract

Following a procedure recently utilized by Accioly et al. to obtain the D-dimensional interparticle potential energy for electromagnetic models in the nonrelativistic limit, and relaxing the condition assumed by the authors concerning the conservation of the external current, the prescription found out by them is generalized so that dual models can also be contemplated. Specific models in which the interaction is mediated by a spin-0 particle described first by a vector field and then by a higher-derivative vector field, are analyzed. Systems mediated by spin-1 particles described, respectively, by symmetric rank-2 tensors, symmetric rank-2 tensors augmented by higher derivatives, and antisymmetric rank-2 tensors, are considered as well.