确定空间非局部算子有限体积效应的模型无关框架
A model-independent framework for determining finite-volume effects of spatially nonlocal operators
摘要：
我们提出了一个独立于模型的框架来确定有限体积修正的空间分离的电流-电流算子的矩阵元素。我们定义这些矩阵元素的康普顿类振幅，即振幅耦合单粒子状态通过两个电流插入。我们表明，这些矩阵元的红外行为是由单粒子极，这是近似的弹性形状因子的最低位强子。因此，给定有关弹性形状因子的晶格数据，有限体积效应可以非微扰地估计，而无需求助于有效场论。为了说明的目的，我们调查的影响，提出的形式主义一类标量理论在二维和四维。
英文摘要：
We present a model-independent framework to determine finite-volume corrections of matrix elements of spatially-separated current-current operators. We define these matrix elements in terms of Compton-like amplitudes, i.e. amplitudes coupling single-particle states via two current insertions. We show that the infrared behavior of these matrix elements is dominated by the single-particle pole, which is approximated by the elastic form factors of the lowest-lying hadron. Therefore, given lattice data on the relevant elastic form factors, the finite-volume effects can be estimated non-perturbatively and without recourse to effective field theories. For illustration purposes, we investigate the implications of the proposed formalism for a class of scalar theories in two and four dimensions.
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