$1+1$维晶格模型中的多粒子相互作用
Multiple-particle interaction in $1+1$ dimensional lattice model
摘要：
在二维复杂$ϕ^4$格点模型中研究了有限体积多粒子相互作用。二维时空中$ϕ^4$模型解析解的存在性使其成为数值研究多粒子相互作用有限体积效应的理想模型。从蒙特卡罗模拟中提取的多个粒子的光谱在几个移动框架的各种晶格。在$ϕ^4$理论中，多粒子散射的$S$矩阵完全由两个基本参数决定：单粒子质量和两对两粒子相互作用的耦合强度。这两个参数是通过研究单粒子和双粒子谱来确定的。由于在$ϕ^{4}$模型中没有衍射效应，因此以简单的解析形式给出了三粒子量子化条件。模拟得到的三粒子能谱与精确解的预测结果有很好的一致性。
英文摘要：
Finite volume multiple-particle interaction is studied in a two-dimensional complex $ϕ^4$ lattice model. The existence of analytical solutions to the $ϕ^4$ model in two-dimensional space and time makes it a perfect model for the numerical study of finite volume effects of multi-particle interaction. The spectra from multiple particles are extracted from the Monte Carlo simulation on various lattices in several moving frames. The $S$-matrix of multi-particle scattering in $ϕ^4$ theory is completely determined by two fundamental parameters: single particle mass and the coupling strength of two-to-two particle interaction. These two parameters are fixed by studying single-particle and two-particle spectra. Due to the absence of the diffraction effect in the $ϕ^{4}$ model, three-particle quantization conditions are given in a simple analytical form. The three-particle spectra from simulation show remarkable agreement with the prediction of exact solutions.
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