Faddeev equations in one-dimensional problems with resonant interactions

TL;DR

This paper simplifies the complex three-boson problem with resonant multichannel interactions in one dimension by reducing it to a single-channel Faddeev-Lovelace equation and regularizing it through algebraic techniques.

Contribution

It introduces a method to reduce multichannel three-boson interactions to a single-channel equation and regularizes it using algebraic properties of singularities.

Findings

Successfully reduces multichannel problem to single-channel equation

Provides a regularization technique for singularities in the equation

Facilitates analysis of one-dimensional bosonic systems with resonant interactions

Abstract

A problem of three one-dimensional bosons with resonant multichannel interactions is considered. The problem is reduced to a single-channel Faddeev-Lovelace equation by elimination of the closed and output channels. The equation is regularized using algebraic properties of their singularities.