AI 中文总结
该研究将广义主丛理论应用于协变拉格朗日场论，通过回顾相关定义、给出联络特征、考虑经典场论框架下的广义主联络等，发展广义杨 - 米尔斯理论，表明向量丛是广义主丛例子，还能恢复广义相对论的 vierbein 表述，暗示引力规范理论。
AI 中文摘要
作为广义主丛理论在协变拉格朗日场论中的应用，我们旨在发展广义规范理论的一个实例，以期为杨 - 米尔斯理论和广义相对论提供统一语言。回顾李群纤维丛和广义主丛的基本定义后，给出李群纤维丛联络和广义主联络的水平提升及局部特征。接着在经典场论框架下考虑广义主联络的运动学和动力学，引出广义杨 - 米尔斯理论概念。最后表明向量丛是广义主丛的例子，向量丛上的广义主联络是由基本焊接形式给出的仿射联络。在适当假设下能在此框架恢复（真空）广义相对论的 vierbein 表述，暗示了一种（广义）引力规范理论。
英文摘要
As an application of the generalized principal bundle theory to covariant Lagrangian field theories, we aim at the development of an instance of generalized gauge theories, with the prospect of a unifying language for Yang-Mills theories and General Relativity. After reviewing the basic definitions of Lie group fiber bundles and generalized principal bundles, we provide horizontal lift and local characterizations of Lie group fiber bundle connections and generalized principal connections. Subsequently, we consider in the framework of classical field theories the kinematics and dynamics sides of generalized principal connections, which lead to a proposed notion of generalized Yang-Mills theories. Finally, we show how vector bundles are examples of generalized principal bundles and that a generalized principal connection on a vector bundle is an affine connection given in terms of basic soldering forms. We are able to recover, under appropriate assumptions, the Vielbein formulation of (vacuum) General Relativity in this setting, hinting at a (generalized) gauge theory of gravity.
Comments11 pages, 0 figures, presented at the conference school "Foundations of General-Relativistic Gauge Field Theory" - 17-19 March, 2026 - Politecnico di Torino, Italy
Journal refPoS FGRGFT2026 (2026), 010
