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Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles

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arxiv 1701.07465 v2 pith:6C42NCGQ submitted 2017-01-25 hep-lat nucl-th

Raúl A. Briceño , Maxwell T. Hansen , Stephen R. Sharpe This is my paper · ORCID
classification hep-latnucl-th
keywords textbfparticlesrelativisticscalarsystemsbelowconditionfinite-volume
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abstract

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicity $L$. This gives the relation between the finite-volume spectrum and the infinite-volume $\textbf 2 \to \textbf 2$, $\textbf 2 \to \textbf 3$ and $\textbf 3 \to \textbf 3$ scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass $m$, whose center of mass energy lies below the four-particle threshold, and for which the two-particle $K$ matrix has no singularities below the three-particle threshold. The quantization condition is exact up to corrections of the order $\mathcal{O}(e^{-mL})$ and holds for any choice of total momenta satisfying the boundary conditions.

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Cited by 3 Pith papers

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