论文标题
$ S $矩阵Unitarity的三体散射和量化条件
Three-body scattering and quantization conditions from $S$ matrix unitarity
论文作者
论文摘要
文献中已经提出了两种方法，这些方法将相对论的三粒子散射幅度与晶格QCD光谱联系起来 - ``相对论有效的现场理论''方法和``有限量 - 数量单位性''方法。尽管两种方法在各种作品中都相等，但尚未显示如何直接从$ s $矩阵Unitarity到达相对论有效的现场理论。在这项工作中，我们提供了一个简单的证明，证明了直接来自单位性的散射方程的相对论有效田间理论形式。然后，我们由有限体积的单位性方法进行，然后假设一组量化条件将有限体积的能源光谱与$ k $矩阵相关联，该矩阵驱动散射方程中的短距离物理学，从而获得了三个相同粒子的所有先前已知的结果。这项工作还提出了新的关系，该关系为将结果推广到任意系统提供了新的途径。
Two methodologies have been presented in the literature which connect relativistic three-particle scattering amplitudes with lattice QCD spectra -- the ``relativistic effective field theory'' approach and the ``finite-volume unitarity'' method. While both methods have been shown to be equivalent in various works, it has not been shown how to arrive at the relativistic effective field theory results directly from $S$ matrix unitarity. In this work, we provide a simple proof of the relativistic effective field theory form of the scattering equations directly from unitarity. Motivated by the finite-volume unitarity approach, we then postulate a set of quantization conditions which relate the finite-volume energy spectra to the $K$ matrices which drive the short-distance physics in the scattering equations, obtaining all previously known results for three identical particles. This work also presents new relations which provide a new pathway to generalize the results to arbitrary systems.
