Flow equation of functional renormalization group for three-body scattering problems

TL;DR

This paper develops a new flow equation within the functional renormalization group framework for three-body scattering in fermionic systems, aligning it with established integral equations and clarifying its relation to the Skornyakov and Ter-Martirosyan equation.

Contribution

The paper introduces a novel and correct flow equation for three-body scattering in fermionic systems, ensuring consistency with Dyson-Schwinger and Skornyakov-Ter-Martirosyan equations.

Findings

The new flow equation is consistent with existing integral equations.

It clarifies the relation to the Skornyakov and Ter-Martirosyan equation.

The approach advances understanding of three-body scattering in fermionic systems.

Abstract

Functional renormalization group (FRG) is applied to the three-body scattering problem in the two-component fermionic system with an attractive contact interaction. We establish a new and correct flow equation on the basis of FRG and show that our flow equation is consistent with integral equations obtained from the Dyson-Schwinger equation. In particular, the relation of our flow equation and the Skornyakov and Ter-Martirosyan equation for the atom-dimer scattering is made clear.