One spatial dimensional finite volume three-body interaction for a short-range potential

Abstract

In this work, we use McGuire's model to describe scattering of three spinless identical particles in one spatial dimension, we first present analytic solutions of Faddeev's equation for scattering of three spinless particles in free space. The three particles interaction in finite volume is derived subsequently, and the quantization conditions by matching wave functions in free space and finite volume are presented in terms of two-body scattering phase shifts. The quantization conditions obtained in this work for short range interaction are Lüscher's formula like and consistent with Yang's results in \cite{Yang:1967bm}.

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Cited by in corpus (5)

• Value of the axial-vector coupling strength in $\beta$ and $\beta \beta$ decays: A review
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Three-body Unitarity in the Finite Volume
• Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
• An numerical approach for finite volume three-body interaction