发表机构
São Paulo State University (UNESP), School of Engineering and Sciences（圣保罗州立大学（UNESP）工程与科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出三阶幂零的形变外导数，其诱导的上同调结构分岔使庞加莱引理失效，并将框架应用于四维有效场论，通过纯几何机制生成电弱与普朗克标度的层级。
AI 中文摘要
受自旋结构的形变及其几何意义的启发，我们研究了一种三阶幂零算子形式的形变外导数。这种高阶微分结构诱导了局部标架的非完整重标度，并导致相关上同调结构的分岔，产生两种不同的闭性与正合性概念。我们证明庞加莱引理在两种情形下均不成立，因此闭的形变形式即使在局部也未必是正合的。随后我们将所得框架应用于四维有效场论，证明形变参数的常数饱和可通过纯几何机制产生电弱标度与基本普朗克标度之间的层级，无需引入额外空间维度。
英文摘要
Motivated by deformations of spin structures and their geometric implications, we study a deformed exterior derivative, which is a third-order nilpotent operator. This higher-order differential structure induces an anholonomic rescaling of the local frame and leads to a bifurcation of the associated cohomological structure, with two distinct notions of closedness and exactness. We prove that the Poincaré Lemma fails in both sectors, so that closed deformed forms need not be exact even locally. We then apply the resulting framework to a four-dimensional effective field theory and show that a constant saturation of the deformation parameter can generate a hierarchy between the electroweak and fundamental Planck scales through a purely geometric mechanism, without introducing extra spatial dimensions.
Comments12 pages, no figures
