论文标题
非扰动QCD的反问题方法：基础
Inverse Problem Approach for Non-Perturbative QCD: Foundation
论文作者
论文摘要
我们提出了一个新型的理论框架来计算非扰动QCD数量。它始于量子场理论的分散关系，分离高能和低能量表，并使用已知的扰动理论来解决未知的非扰动数量通过反问题解决。我们证明，分散关系的逆问题是不合适的，具有独特但不稳定的解决方案。正则化方法必须用于获取稳定的近似解决方案。该方法基于严格的数学，而没有任何人为的假设。我们已经测试了一些玩具模型，以生动地显示逆问题的主要特征。可以发现这种方法可以系统地提高解决方案的精度。
We propose a novel theoretical framework to calculate the non-perturbative QCD quantities. It starts from the dispersion relation of quantum field theory, separating the high-energy and low-energy scales and using the known perturbative theories to solve the unknown non-perturbative quantities by the inverse problem. We prove that the inverse problem of dispersion relation is ill-posed, with unique but unstable solutions. The regularization methods must be used to get the stable approximate solutions. The method is based on the strict mathematics, without any artificial assumptions. We have test some toy models to vividly show the main features of the inverse problem. It can be found that this approach can systematically improve the precision of the solutions.
