Interactions between delta-like sources and potentials

TL;DR

This paper analyzes how delta-like sources interact with semi-transparent mirrors, deriving modified propagators and potentials, including classical image methods and specific attractive potentials, in various dimensions.

Contribution

It provides a general framework for calculating interactions involving delta-like sources and hyperplane mirrors, extending known image methods to arbitrary dimensions.

Findings

Modified scalar boson propagator with mirror effects

Classical interaction results including image method

Derived attractive potential in 3+1 dimensions

Abstract

The modified scalar boson propagator due to the presence of a hyperplane semi-transparent mirror is computed. From this, the classical interaction between static charges and the mirror is investigated employing delta-like potentials and sources. Although the calculations for hyperplane mirrors are performed in arbitrary dimensions, and in a completely general way, it is shown that the results give rise to the usual image method as a particular case. The interaction between a point-like mirror and a point-like source is also considered in $3+1$ dimensions, where a central $1/R^{2}$ attractive potential is also obtained as a special case.