On revolutionizing quantum field theory with Tomita’s modular theory
On revolutionizing quantum field theory with Tomita’s modular theory
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论用富田模理论彻底改变量子场论
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
H. Borchers
中科院分区：
文献类型：
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作者：
Erwin Schrödinger International;H. Borchers
在 Haag [局域量子物理学（Springer Verlag，柏林，1992）] 的关于局域量子场论的书中，主要结果是通过 C*- 和 W*- 代数理论的旧方法获得的。一个巨大的进步，特别是在 W* 代数理论方面，归功于 Tomita 发现了模希尔伯特代数理论 [Quasi-standard von Neumann algebras, Preprint (1967)]。由于基本概念的抽象性，该理论直到九十年代初才成为量子场论的一种技术（除了一些零星的结果）。在这次审查中，我们将收集迄今为止所获得的结果，并在最后讨论未来的一些问题。第一部分将介绍技术工具。然后在第二部分中将解释两个概念，半边翻译和半边模块包含。这些概念彻底改变了量子场论的处理。明确已知模块组的示例是......
In the book of Haag [Local Quantum Physics (Springer Verlag, Berlin, 1992)] about local quantum field theory the main results are obtained by the older methods of C*- and W*-algebra theory. A great advance, especially in the theory of W*-algebras, is due to Tomita’s discovery of the theory of modular Hilbert algebras [Quasi-standard von Neumann algebras, Preprint (1967)]. Because of the abstract nature of the underlying concepts, this theory became (except for some sporadic results) a technique for quantum field theory only in the beginning of the nineties. In this review the results obtained up to this point will be collected and some problems for the future will be discussed at the end. In the first section the technical tools will be presented. Then in the second section two concepts, the half-sided translations and the half-sided modular inclusions, will be explained. These concepts have revolutionized the handling of quantum field theory. Examples for which the modular groups are explicitly known are...