arXiv 2202.082632022-02math.GRhep-th

Yang-Mills理论的两个版本

Integer versions of Yang-Mills theory

R. A. Wilson

备注：: v3: 20 pages; added sections on the equivalence principle, quantum gravity, and symmetry-breaking. v2: added sections on the derivation of effective field theories and the standard model from the proposed fundamental model

摘要：

在最近的一篇论文中，特胡夫特要求杨-米尔斯理论的整数版本，相信这是宇宙在普朗克尺度下的真实状态。具体地说，他要求标准模型的规范群的整数版本。这样的群在100多年前就被完全分类了，在这里，我详细介绍了我认为可以回答特胡夫特问题的具体情况的群论和表示论（以及一些物理学）。

英文摘要：

In a recent paper, 't Hooft asks for an integer version of Yang-Mills theory, in the belief that this is the way the universe really is at the Planck scale. Specifically, he asks for an integer version of the gauge group of the standard model. Such groups were completely classified more than 100 years ago, and here I detail the group theory and representation theory (and some of the physics) of the specific case that I believe answers 't Hooft's question.

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