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 (38)

• Scattering processes and resonances from lattice QCD
• 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
• Three-body spectrum in a finite volume: the role of cubic symmetry
• Three pion spectrum in the $I=3$ channel from lattice QCD
• Three-body unitarity versus finite-volume ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ spectrum from lattice QCD
• Numerical study of the relativistic three-body quantization condition in the isotropic approximation
• Energy shift of the three-particle system in a finite volume
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• Three-body interactions from the finite-volume QCD spectrum
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• $DDK$ system in finite volume
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• Spurious poles in a finite volume
• Toward extracting scattering phase shift from integrated correlation functions on quantum computers
• 3-body quantization condition in a unitary formalism
• Three particles on the lattice
• Transmission coefficient of interacting few-body system in one dimensional space