标题： 预几何一阶杨-米尔斯理论 显示英文标题

标题： Pregeometric First Order Yang-Mills Theory

摘要： 粒子和基本相互作用的标准描述 crucially 基于一个规则的度规背景。用微分几何的语言来说，这种依赖性通过霍奇星算子对偶化编码到作用量中。因此，在度规退化的预几何区域，标量和杨-米尔斯作用量的传统形式会失效。这表明可以使用一阶形式论，在这种形式论中，度规可以从更基本的组分中浮现出来，并且理论可以一致地扩展到预几何相。我们系统地探索了一阶形式论的不同实现和解释，发现基本矢量或旋量亚结构带来了连续磁化和极化作为积分常数。这一效应类似于最近重力的一个自对偶公式中宇宙学暗物质部门的描述，而一阶杨-米尔斯理论得到的相似形式为统一提供了新的路径。 显示英文摘要

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.