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arXiv · 2607.19709

Point-Like Charges and Dirichlet Boundary Conditions in a Nonlocal Scalar Field Theory

L. H. C. Borges·C. Filgueiras·F. A. Barone·A. A. Nogueira
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Abstract

In this paper, we investigate novel classical non-local effects in scalar field theory arising from the presence of external sources and a material boundary. Specifically, we consider a model in which the standard Klein-Gordon field theory is modified by a non-local term. First, we analyze the interaction between stationary field sources modeled as point-like scalar charges. In specific configurations, the resulting interparticle potential reduces to the Cornell form. Then, we examine the model in the presence of a Dirichlet plane, computing both the scalar field propagator and the interaction force between the Dirichlet plane and a point-like scalar charge. Additionally, we demonstrate the failure of the image method in this non-local context and compare our results with those obtained in non-local electrodynamics and in the standard Klein-Gordon field theory.

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L. H. C. Borges, C. Filgueiras, F. A. Barone, A. A. Nogueira. 2026-07-22. Point-Like Charges and Dirichlet Boundary Conditions in a Nonlocal Scalar Field Theory. https://arxiv.org/abs/2607.19709

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