论文标题
广义框架束上的狄拉克纺纱器：爱因斯坦 - 卡丹 - 迪拉克理论的框架束公式
Dirac Spinors on Generalised Frame Bundles: a frame bundle formulation for Einstein-Cartan-Dirac theory
论文作者
论文摘要
我们阐明了Hélein和Vey在Einstein-Cartan引力的构想中获得的结构，该结构是从框架束上提出的，从无结构可区分的10个manifold开始（ARXIV：1508.07765V2 [MATH-PH]）。获得的结构在局部等效于框架束。我们表明，在全球假设下，形式主义允许产生各种原理，该原理在基本歧管上诱导框架束结构，并在基本歧管上诱导纤维。我们对该模型的看法使我们能够将爱因斯坦 - 卡丹模型扩展到爱因斯坦 - 卡丹 - 迪拉克理论，其中包括与扭转场耦合的狄拉克纺纱场。
We clarify the structure obtained in Hélein and Vey's proposition for a variational principle for the Einstein-Cartan gravitation formulated on a frame bundle starting from a structure-less differentiable 10-manifold (arXiv:1508.07765v2 [math-ph]). The obtained structure is locally equivalent to a frame bundle. We show that under global hypotheses the formalism allows to produce variational principles which induce a frame bundle structure with a fibration over a base manifold and a variational principle on the base manifold. Our perspective on the model allows us to extend the Einstein-Cartan model to the Einstein-Cartan-Dirac theory which includes a Dirac spinor field coupled to the torsion field.
