Abstract
We discuss the quantum-mechanical scattering of a massless scalar field on a δ-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 δ-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 δ-potential well. In the limit of vanishing non-locality, we recover the standard results of local field theory.
Highlights
Solvable problems have played an important role in quantum mechanics, especially at the early stage of its development [1,2,3,4,5,6,7]
We consider the scattering of a particle on a δ-like potential in the framework of a socalled ghost-free scalar field theory, which belongs to a class of non-local generalizations of relativistic field theories that have recently been studied quite extensively [8,9,10,11,12]
Our starting point was a two-dimensional theory of a massless scalar field in the presence of a static δ-like potential
Summary
Solvable problems have played an important role in quantum mechanics, especially at the early stage of its development [1,2,3,4,5,6,7] Such problems typically give analytical results for scattering amplitudes and the energies of bound states, and they allow one to analyze non-perturbative aspects of these problems, for example non-analyticity. We consider the scattering of a particle on a δ-like potential in the framework of a socalled ghost-free scalar field theory, which belongs to a class of non-local generalizations of relativistic field theories that have recently been studied quite extensively [8,9,10,11,12]. In this letter we discuss a rather simple problem related to the linear regime of ghost-free theory: scattering and
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