Quantum scattering on a delta potential in ghost-free theory

TL;DR

This paper analyzes how ghost-free non-local modifications to quantum theory affect scattering on a delta potential, revealing unique high-frequency transmission and reflection behaviors not seen in local theories.

Contribution

It provides analytic solutions for scattering coefficients in ghost-free theories and highlights distinctive non-local effects on scattering properties.

Findings

Transmission tends to unity at high frequencies for strong potentials

Existence of a critical potential strength for total reflection

Recovery of local theory results as non-locality vanishes

Abstract

We discuss the quantum-mechanical scattering of a massless scalar field on a $\delta$-potential in a ghost-free theory and obtain analytic solutions for the scattering coefficients. Due to the non-locality of the ghost-free theory the transmission coefficient tends to unity for frequencies much larger than the inverse scale of non-locality, even for infinitely strong potentials. At the same time there exists a critical strength of the $\delta$-potential barrier below which there is always a frequency that is totally reflected. These scattering properties in ghost-free theories are quite generic and distinguish them from local field theories. Moreover, we study quasi-normal states that are present for the $\delta$-potential well. In the limit of vanishing non-locality, we recover the standard results of local field theory.