通过重整化关联理论
Relating Theories via Renormalization
摘要：
重整化方法的目的是连接描述不同长度尺度的物理过程的理论，从而连接物理科学中的不同理论。今天使用的重整化方法是一百五十年来对热物理和相变的科学研究的产物。物质的不同相态表现出由突然的相变分离的性质不同的行为。这些质的差异似乎存在于实验观察到的凝聚态系统中。但是，统计力学中的“扩展奇点定理”表明，急剧的变化只能发生在无限大的系统中。从一个相位到另一个相位的突然变化是由在无限长的距离上显示相关性的波动发出的信号，并且由显示代数衰减以及热力学导数和测量的系统参数中的各种奇异性和无穷大的关联函数测量。重正化方法最初是在场论中发展起来的，目的是为了解决在小尺度和大尺度下由明显发散引起的困难。相变的重整化（半）群理论是由Kenneth G. Wilson在1971年提出的基于早期在相变和耦合依赖于来自场论的空间尺度的背景下发展的标度和普适性的思想。重整化思想的基础是有序涨落区域之间的相关性。Wilson理论是研究相变的第一个与扩展奇点定理相一致的方法。一些历史的研究，这些相关性和奇异性的叙述，随着历史的重整化和相关的概念的标度和普遍性。应用程序进行了总结。
英文摘要：
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is the outgrowth of one hundred and fifty years of scientific study of thermal physics and phase transitions. Different phases of matter show qualitatively different behavior separated by abrupt phase transitions. These qualitative differences seem to be present in experimentally observed condensed-matter systems. However, the "extended singularity theorem" in statistical mechanics shows that sharp changes can only occur in infinitely large systems. Abrupt changes from one phase to another are signaled by fluctuations that show correlation over infinitely long distances, and are measured by correlation functions that show algebraic decay as well as various kinds of singularities and infinities in thermodynamic derivatives and in measured system parameters. Renormalization methods were first developed in field theory to get around difficulties caused by apparent divergences at both small and large scales. The renormalization (semi-)group theory of phase transitions was put together by Kenneth G. Wilson in 1971 based upon ideas of scaling and universality developed earlier in the context of phase transitions and of couplings dependent upon spatial scale coming from field theory. Correlations among regions with fluctuations in their order underlie renormalization ideas. Wilson's theory is the first approach to phase transitions to agree with the extended singularity theorem. Some of the history of the study of these correlations and singularities is recounted, along with the history of renormalization and related concepts of scaling and universality. Applications are summarized.
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