# Ground state energy of a dilute Bose gas with three-body hard-core interactions

## TL;DR

This paper calculates the lowest energy state of a dilute Bose gas with three-body hard-core interactions, confirming a theoretical prediction.

## Contribution

The paper provides a matching upper bound for the ground state energy, resolving the leading order for three-body hard-core interactions.

## Key findings

- An upper bound on the ground state energy was derived using a Jastrow factor.
- The result matches the previously established lower bound, confirming the leading order.
- The method can be adapted for systems with combined two- and three-body interactions.

## Abstract

We consider a gas of bosons interacting through a three-body hard-core potential in the thermodynamic limit. We derive an upper bound on the ground state energy of the system at the leading order using a Jastrow factor. Our result matches the lower bound proven by Nam–Ricaud–Triay (J Math Phys 63:071903, 2022) and therefore resolves the leading order. Moreover, a straightforward adaptation of our proof can be used for systems interacting via combined two-body and three-body interactions to generalise Theorem 1.2 from (Ann. Henri Poincaré, 2026) to hard-core potentials.