Double-delta potentials: one dimensional scattering. The Casimir effect and kink fluctuations

TL;DR

This paper investigates one-dimensional quantum scattering and field theories with delta potentials, revealing connections to the Casimir effect and sine-Gordon kink fluctuations, and explores absorbent plates via delta wells.

Contribution

It establishes links between delta potentials, the Casimir effect, and sine-Gordon kink fluctuations within a unified framework under Dirichlet boundary conditions.

Findings

Two delta potentials relate to the Casimir effect.

Delta potentials plus Pösch-Teller well describe sine-Gordon kink fluctuations.

Delta wells can model absorbent plates despite non-unitarity.

Abstract

The path is explored between one-dimensional scattering through Dirac-$\delta$ walls and one-dimensional quantum field theories defined on a finite length interval with Dirichlet boundary conditions. It is found that two $\delta$'s are related to the Casimir effect whereas two $\delta$'s plus the first transparent P$\ddot{\rm o}$sch-Teller well arise in the context of the sine-Gordon kink fluctuations, both phenomena subjected to Dirichlet boundary conditions. One or two delta wells will be also explored in order to describe absorbent plates, even though the wells lead to non unitary Quantum Field Theories.