arXiv 2202.056572022-02-11hep-thgr-qc

准几何一阶Yang-Mills理论

Pregeometric First Order Yang-Mills Theory

Priidik Gallagher, Tomi Koivisto, Luca Marzola

备注：: 33 pages, no figures
DOI：: 10.1103/PhysRevD.105.125010

摘要：

粒子和基本相互作用的标准描述是基于规则的度规背景的。在微分几何的语言中，这种依赖性通过霍奇星对偶被编码到动作中。因此，传统形式的标量和杨-米尔斯行动打破了在一个pregeometric制度，其中的度规是退化。这表明使用一阶形式主义，其中度量可能出现从更基本的成分和理论可以一贯地扩展到前几何阶段。我们系统地探讨了一阶形式主义的不同实现和解释，发现一个基本矢量或旋量子结构带来连续磁化和极化作为积分常数。这种效应类似于最近的引力自对偶公式中对宇宙学暗区的描述，一阶杨-米尔斯理论得到的类似形式表明了走向统一的新途径。

英文摘要：

The standard description of particles and fundamental interactions is crucially based on a regular metric background. In the language of differential geometry, this dependence is encoded into the action via Hodge star dualization. As a result, the conventional forms of the scalar and Yang-Mills actions break down in a pregeometric regime where the metric is degenerate. This suggests the use of first order formalism, where the metric may emerge from more fundamental constituents and the theory can be consistently extended to the pregeometric phase. We systematically explore different realizations and interpretations of first order formalism, finding that a fundamental vector or spinor substructure brings about continuum magnetization and polarization as integration constants. This effect is analogous to the description of the cosmological dark sector in a recent self-dual formulation of gravity, and the similar form obtained for the first order Yang-Mills theory suggests new paths toward unification.

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摘要：

英文摘要：

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