Construction of exactly solvable quantum models of Calogero and Sutherland type with translation invariant four-particle interactions

TL;DR

This paper develops exactly solvable quantum models for four particles with translation-invariant interactions, applicable on a line or circle, expanding the class of solvable many-body systems.

Contribution

It introduces new quantum models with four-particle interactions that are exactly solvable and translation invariant, extending previous models in the field.

Findings

Models are solvable for both line and circle configurations.

Inclusion of four-particle interactions maintains exact solvability.

Models exhibit translation invariance in interactions.

Abstract

We construct exactly solvable models for four particles moving on a real line or on a circle with translation invariant two- and four-particle interactions.