超复数代数纤维丛上的规范理论
Gauge Theory on Fiber Bundle of Hypercomplex Algebras
AI总结：
本文提出在超复数代数纤维丛上构建新规范理论，发现由于标量场及其真空在$\mathbb{Z}_2$对称性下固有的偶宇称，可优先动态选择某一简并真空，从而解决真空选择问题。
摘要：
我引入了一种构造纤维丛的方法，其纤维由超复数代数给出并由适当的结构群编织，并提出可以在这种超复数纤维丛上构建一种新颖的规范理论。在这项工作中，我旨在回答一个关于自然如何在简并的物理真空（称为真空选择问题）中选择一个优先真空的问题。最终，我发现了不可穿透的畴壁的存在，它禁止了两个真空之间的相变。具体而言，我发现在该理论中，对于类Higgs标量势，两个简并物理真空中的某一个特定真空可以被优先动态选择，这是由于标量场及其真空在$\mathbb{Z}_2$对称性下固有的偶宇称，即使其标量势在标量场的奇宇称和偶宇称变换下均被给定为$\mathbb{Z}_2$对称的。这意味着真空选择问题可以在这个规范理论中得到解决。我建议这项工作可能是解决自然界所取的真实物理真空理论起源的一个门户。
英文摘要：
I introduce a way of constructing a fiber bundle whose fibers are given by hypercomplex algebras and woven by appropriate structure group, and present that a novel gauge theory can be built on the hypercomplex fiber bundle. In this work, I aim to answer a question about how nature selects one preferred vacuum among degenerate physical vacua, called {\it vacuum selection problem}. In the end, I found presence of the impenetrable domain wall that prohibits phase transition between the two vacua. To be specific, I found that in this theory, one particular vacuum between two degenerate physical vacua for Higgs-like scalar potential can be dynamically chosen with priority due to intrinsic even parity of both a scalar field and its vacuum under a $\mathbb{Z}_2$ symmetry, even though its scalar potential is given to be $\mathbb{Z}_2$-symmetric under both odd- and even-parity transformations of the scalar field. This means that the vacuum selection problem can be resolved in this gauge theory. I suggest that this work may be a gateway to addressing the theoretical origin of the true physical vacuum that nature takes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
