Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles
Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles
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DOI：
10.1103/physrevd.95.074510
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发表时间：
2017-01
影响因子：
5
通讯作者：
R. Briceño;M. Hansen;S. Sharpe
中科院分区：
文献类型：
--
作者：
R. Briceño;M. Hansen;S. Sharpe
在相对论量子场论中，我们推导出了限制在周期性为$L$的立方空间体积中的相同标量粒子的耦合两粒子和三粒子系统所满足的量子化条件。这给出了有限体积谱与无限体积$\textbf 2 \to \textbf 2$，$\textbf 2 \to \textbf 3$和$\textbf 3 \to \textbf 3$散射振幅之间的关系。这一结果适用于由非零质量m的标量粒子组成的相对论系统，其质心能量低于四粒子阈值，并且两粒子K矩阵在三粒子阈值以下没有奇点。量子化条件是精确的，直到阶数$\mathcal{O}（e^{-mL}）$的修正，并且对于满足边界条件的总动量的任何选择都成立。
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.