Three fermions in a box

TL;DR

This paper calculates finite-volume effects for three identical spin-1/2 fermions with short-range repulsive interactions using perturbation theory, providing results for ground states in various cubic symmetry representations.

Contribution

It introduces a perturbative method to analyze finite-volume effects for three fermions, detailing ground state energies across different cubic symmetries.

Findings

Finite-volume energy shifts are computed for three fermions.

Results are provided for ground states in A_1, T_1, and E representations.

The analysis applies standard perturbation theory in powers of 1/L.

Abstract

I calculate finite-volume effects for three identical spin-1/2 fermions in a box assuming short-ranged repulsive interactions of `natural size'. This analysis employs standard perturbation theory in powers of 1/L, where L^3 is the volume of the box. I give results for the ground states in the A_1, T_1, and E cubic representations.