Three-particle States in Nonrelativistic Four-fermion Model

TL;DR

This paper investigates a nonrelativistic four-fermion model, demonstrating how specific renormalization and boundary conditions yield a well-defined Hamiltonian and exact solutions for few-particle states, including three-particle bound states.

Contribution

It introduces a renormalization scheme with a Lambda-cut-off that ensures a self-adjoint Hamiltonian and derives exact three-particle solutions from two-particle data.

Findings

Self-adjoint, semi-bounded Hamiltonian achieved in all particle sectors.

Exact solutions for two-particle sector fully determine three-particle problem.

Renormalized Faddeev equations with Fredholm properties derived for bound states.

Abstract

On a nonrelativistic contact four-fermion model we have shown that the simple Lambda-cut-off prescription together with definite fine-tuning of the Lambda dependency of "bare"quantities lead to self-adjoint semi-bounded Hamiltonian in one-, two- and three-particle sectors. The fixed self-adjoint extension and exact solutions in two-particle sector completely define three-particle problem. The renormalized Faddeev equations for the bound states with Fredholm properties are obtained and analyzed.