Bound states in nonrelativistic four-fermion interaction model

TL;DR

This paper investigates bound states in a non-relativistic four-fermion interaction model using Bethe-Salpeter equations, revealing a Goldstone mode due to spontaneous symmetry breaking.

Contribution

It provides a closed-form derivation of Bethe-Salpeter equations and identifies a Goldstone mode associated with SU(2) symmetry breaking in the model.

Findings

Existence of bound states in the model.

Closed-form Bethe-Salpeter equations derived.

Goldstone mode identified due to symmetry breaking.

Abstract

The bound states of two particles are studied in frames of non-relativistic quantum field model with current $\times$ current type interaction by analyzing the Bethe-Salpeter amplitudes. The Bethe-Salpeter equations are obtained in closed form. The existence of Goldstone mode corresponding to the spontaneous breaking of additional SU(2) symmetry of the model is revealed.