多通道Lüscher行列式条件的特征值分解有效解
Efficient solution of the multi-channel Lüscher determinant condition through eigenvalue decomposition
摘要：
我们提出了一种方法，有效地找到解决方案的Lüscher的量子化条件，该方程涉及两个粒子散射振幅的离散谱的状态在一个周期性的空间体积的有限程度，如目前在格点量子色动力学。所提出的方法是基于耦合通道和分波的空间中的本征值分解，这被证明有几个理想的和简化的功能，是非常有益的，当考虑简单的无自旋粒子的弹性散射的问题。我们说明了一个玩具模型的矢量矢量散射具有高密度的解决方案，并与应用程序的明确的格点量子色动力学能级数据描述$J^P=1^-$和$1^+$散射在几个耦合通道的方法。
英文摘要：
We present a method for efficiently finding solutions of Lüscher's quantisation condition, the equation which relates two-particle scattering amplitudes to the discrete spectrum of states in a periodic spatial volume of finite extent such as that present in lattice QCD. The approach proposed is based on an eigenvalue decomposition in the space of coupled-channels and partial-waves, which proves to have several desirable and simplifying features that are of great benefit when considering problems beyond simple elastic scattering of spinless particles. We illustrate the method with a toy model of vector-vector scattering featuring a high density of solutions, and with an application to explicit lattice QCD energy level data describing $J^P=1^-$ and $1^+$ scattering in several coupled channels.
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