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Woit · 2025-10-20
已登记出处中的最早位置：§39.5 · zh-CN。
来源短摘录与定位
§39.5 · zh-CN · machine_draft · machine-draft-not-reviewed
随后人们尝试取一个能够恢复无限维系统的极限。这样的极限通常是相当奇异的，会导致无限的结果，而处理这些潜在无穷大的过程被称为“重整化(renormalization)”。以能够导致一致且物理上合理的结果的方式取这类极限的技术，通常占据标准量子场论教科书的大部分内容。对于许多理论，人们不知道有任何适当的此类技术，并且猜测也不可能存在任何此类技术。对于另一些理论，有很好的证据表明这样的极限可以被成功取到，但如何做到这一点的细节仍然未知，例如，对于杨-米尔斯规范理论的情形，为严格证明这是可能的而提供了 $1 百万美元的千禧年奖（此情形中的哈密顿量将在第 46 章讨论）。
§39.5 · en · machine_draft · machine-draft-not-reviewed
One then tries to take a limit that recovers the infinite dimensional system. Such a limit will generally be quite singular, leading to an infinite result, and the process of manipulating these potential infinities is called “renormalization”. Techniques for taking limits of this kind in a manner that leads to a consistent and physically sensible result typically take up a large part of standard quantum field theory textbooks. For many theories, no appropriate such techniques are known, and conjecturally none are possible. For others there is good evidence that such a limit can be successfully taken, but the details of how to do this remain unknown, with for instance a $1 million Millenium Prize ofered for showing rigorously this is possible in the case of Yang-Mills gauge theory (the Hamiltonian in this case will be discussed in chapter 46).