The role of scalar current coupling along surfaces

TL;DR

This paper introduces a novel coupling mechanism between a complex scalar field and a planar potential, revealing unique interaction behaviors and boundary conditions in the field solutions.

Contribution

It proposes an exact coupling method via the Klein-Gordon current and analyzes its effects on scalar charge interactions and boundary conditions.

Findings

Complex scalar charge does not interact with the potential.

The potential alters interactions between charges on opposite sides.

Infinite coupling leads to MIT boundary conditions.

Abstract

In this paper we propose a coupling between the complex scalar field and an external Dirac delta-like planar potential. The coupling is achieved through the Klein-Gordon current normal to the plane where the potential is concentrated. The results are obtained exactly and exhibit many peculiarities. We show that a complex scalar charge does not interact with the potential, but the potential modifies the interaction between two scalar charges if they are placed on opposite sides of the planar potential. When the coupling constant between the potential and the field goes to infinity, the classical field solutions satisfy a kind of MIT boundary conditions along the plane where the potential is concentrated.