AI 中文总结
研究非局部标量场论中外部源和物质边界产生的效应，通过修改的克莱因 - 戈登场论模型，分析点状电荷相互作用、狄利克雷平面相关情况，证明镜像法失效并与其他理论比较结果。
AI 中文摘要
本文研究了标量场论中由外部源和物质边界产生的新型经典非局部效应。具体而言，考虑一个通过非局部项修改标准克莱因 - 戈登场论的模型。首先分析了建模为点状标量电荷的静态场源之间的相互作用，在特定配置下，粒子间势简化为康奈尔形式。接着研究了存在狄利克雷平面时的模型，计算了标量场传播子以及狄利克雷平面与点状标量电荷之间的相互作用力。此外，证明了镜像法在此非局部情形下失效，并将结果与非局部电动力学及标准克莱因 - 戈登场论中的结果进行了比较。
英文摘要
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.
