反射边界条件下关联函数的渐近主值与正则化方法
Asymptotic principal values and regularization methods for correlation functions with reflective boundary conditions
摘要：
我们引入了渐近主值的概念，使我们能够处理严格的奇异积分的高阶极点中遇到的各种数量的计算的基础上的真空关联函数。证明了几个关于渐近主值的定理，这些定理可望成为研究和发展奇异积分正则化方法的基础。我们利用这些定理来分析一些正则化方法之间的相互关系，包括一种自然地从渐近主值导出的方法。事实证明，渐近主值的概念及其定理在这种类型的分析中非常有用，提供了一种合适的语言来描述每个正则化方法中丢弃和保留的内容。
英文摘要：
We introduce a concept of asymptotic principal values which enables us to handle rigorously singular integrals of higher-order poles encountered in the computation of various quantities based on correlation functions of a vacuum. Several theorems on asymptotic principal values are proved and they are expected to become bases for investigating and developing some class of regularization methods for singular integrals. We make use of these theorems for analyzing mutual relations between some regularization methods, including a method naturally derived from asymptotic principal values. It turns out that the concept of asymptotic principal values and the theorems for them are quite useful in this type of analysis, providing a suitable language to describe what is discarded and what is retained in each regularization method.
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