论文标题
关于阳米尔斯型理论的最大，通用和完整的扩展
On Maximal, Universal and Complete Extensions of Yang-Mills-Type Theories
论文作者
论文摘要
在本文中，我们继续进行有关粒子物理标准模型扩展的分类计划：Arxiv：2007.01660。当试图对固定的Yang-Mills-type理论的任何类别进行分类时，我们提出了四个互补问题：存在问题，障碍问题，最大问题和普遍性问题。我们证明，所有这些问题都承认了$ s^g $的扩展类别内部纯粹的分类特征。使用此信息，我们表明最大和普遍性是密集的属性，这意味着，如果它们在$ \ Mathcal {e}（s^g; \ hat {g}）$中不满足，则它们处于“单点紧凑”中的“ $ \ Mathcal” $ \ Mathcal {e}（e}（e}） $ \ hat {s} $。我们证明，通过假设选择的公理可以获得另一个最大定理，现在独立于琐碎的扩展$ \ hat {s} $。我们考虑几乎相干扩展的类别，即完整，注入性和回调类型，我们证明存在和阻塞问题具有完整的解决方案。再次使用选择的公理，我们证明这类扩展可以满足第二个最大定理的假设。
In this paper we continue the program on the classification of extensions of the Standard Model of Particle Physics started in arXiv:2007.01660. We propose four complementary questions to be considered when trying to classify any class of extensions of a fixed Yang-Mills-type theory $S^G$: existence problem, obstruction problem, maximality problem and universality problem. We prove that all these problems admits a purely categorical characterization internal to the category of extensions of $S^G$. Using this we show that maximality and universality are dense properties, meaning that if they are not satisfied in a class $\mathcal{E}(S^G;\hat{G})$, then they are in their "one-point compactification" $\mathcal{E}(S^G;\hat{G})\cup \hat{S}$ by a specific trivial extension $\hat{S}$. We prove that, by means of assuming the Axiom of Choice, one can get another maximality theorem, now independent of the trivial extension $\hat{S}$. We consider the class of almost coherent extensions, i.e, complete, injective and of pullback-type, and we show that for it the existence and obstruction problems have a complete solution. Using again the Axiom of Choice, we prove that this class of extensions satisfies the hypothesis of the second maximality theorem.
