论文标题
量子场理论中的不确定问题
Undecidable problems in quantum field theory
论文作者
论文摘要
我们指出，从精确的数学意义上讲，量子场理论中的某些问题是不可决定的。更具体地说，将证明没有算法回答给定的2D超对称拉格朗日理论是否打破超对称性。还将表明，只有当标准的Zermelo-fraenkel设定理论具有选择的公理时，就会有一个特定的2D超对称拉格朗日理论，它会破坏超对称性，这是一致的，这永远无法被证明或反对，因为这是Gödel的第二种不完整理论的结果。本文包括简短而非正式的介绍，讨论了不可证明性现象及其在理论物理学中的以前出现。
We point out that some questions in quantum field theory are undecidable in a precise mathematical sense. More concretely, it will be demonstrated that there is no algorithm answering whether a given 2d supersymmetric Lagrangian theory breaks supersymmetry or not. It will also be shown that there is a specific 2d supersymmetric Lagrangian theory which breaks supersymmetry if and only if the standard Zermelo-Fraenkel set theory with the axiom of choice is consistent, which can never be proved or disproved as the consequence of Gödel's second incompleteness theorem. The article includes a brief and informal introduction to the phenomenon of undecidability and its previous appearances in theoretical physics.
