Ground state energy of the low density Bose gas with three-body interactions

TL;DR

This paper establishes that the leading order ground state energy of a low density Bose gas with three-body interactions is determined by the scattering energy, extending known results from two-body interactions.

Contribution

It provides a rigorous proof for the ground state energy in a Bose gas with three-body interactions, a case not previously fully analyzed.

Findings

Ground state energy is determined by the scattering energy of the three-body potential.

Extends the understanding of Bose gases from two-body to three-body interactions.

Provides a mathematical foundation for future studies on many-body quantum systems.

Abstract

We consider the low density Bose gas in the thermodynamic limit with a three-body interaction potential. We prove that the leading order of the ground state energy of the system is determined completely in terms of the scattering energy of the interaction potential. The corresponding result for two-body interactions was proved in seminal papers of Dyson (1957) and Lieb--Yngvason (1998).