Potential problems with interpolating fields

TL;DR

The paper highlights that interpolating fields can introduce artificial features into potentials, demonstrated through a toy scattering model showing how admixture of channels can produce misleading repulsive cores.

Contribution

It reveals that features like repulsive cores in potentials may originate from the choice of interpolating fields rather than actual system dynamics.

Findings

Potential derived from mixed channels shows a strong repulsive core.

Admixture of closed channels can create artificial features in potentials.

Features in potentials may not reflect true physical interactions.

Abstract

A potential can have features that do not reflect the dynamics of the system it describes but rather arise from the choice of interpolating fields used to define it. This is illustrated using a toy model of scattering with two coupled channels. A Bethe-Salpeter amplitude is constructed which is a mixture of the waves in the two channels. The potential derived from this has a strong repulsive core, which arises from the admixture of the closed channel in the wave function and not from the dynamics of the model.