量子物理学中的无穷概念
Notions of Infinity in Quantum Physics
摘要：
在这篇文章中，我们将回顾希尔伯特空间算子和算子代数中出现的一些无限性概念。这些包括适当的无限性，穆雷冯诺依曼的分类到I型和III型因素和类的F{/o} lner C*-代数，捕捉一些方面的顺从性。我们还将提到这些概念如何在量子力学、量子场论和超选择扇区理论的某些数学方面的描述中重现。我们还证明了正则反对易关系的代数（CAR-代数）属于F{/o} lnerC *-代数类。
英文摘要：
In this article we will review some notions of infiniteness that appear in Hilbert space operators and operator algebras. These include proper infiniteness, Murray von Neumann's classification into type I and type III factors and the class of F{/o} lner C*-algebras that capture some aspects of amenability. We will also mention how these notions reappear in the description of certain mathematical aspects of quantum mechanics, quantum field theory and the theory of superselection sectors. We also show that the algebra of the canonical anti-commutation relations (CAR-algebra) is in the class of F{/o} lner C*-algebras.
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