Impossibility to describe repulsion with contact interaction

TL;DR

This paper discusses the fundamental limitations of contact interactions in modeling repulsive systems, highlighting that such interactions inherently lead to attraction and that cut-offs act as finite range parameters, complicating the description of repulsive Bose gases.

Contribution

It provides a theoretical argument demonstrating the impossibility of representing repulsive interactions with contact interactions and clarifies the role of cut-offs as finite range parameters.

Findings

Contact interactions inherently produce attractive behavior.

Repulsive systems cannot be accurately modeled with contact interactions.

Cut-offs are effectively finite range parameters.

Abstract

Contact interactions always lead to attractive behaviour. Arguments are presented to show why a repulsive interacting system, e.g. Bose gases, cannot be described by contact interactions and corresponding treatments are possibly obscured by the appearance of bound states. The usually used cut-offs are identified as finite range parameters.