论文标题
较高规格理论的构建和示例
Construction and examples of higher gauge theories
论文作者
论文摘要
我们提供了几个较高规格理论的示例，这些示例是针对2BF和3BF模型的BF模型的概括。使用高等类别理论的框架，我们引入了适当的2组和3组，并为相应的约束2BF和3BF理论构建了动作。通过这种方式，我们可以构建动作，描述与爱因斯坦 - 卡丹重力相连的杨米尔，克莱因·戈登，迪拉克，韦伊尔和主要领域的正确动力学。每个动作自然都会分为拓扑部门和具有简单性约束的部门。较高仪表群结构的性质开辟了所有领域非平凡统一的可能性。
We provide several examples of higher gauge theories, constructed as generalizations of a BF model to 2BF and 3BF models with constraints. Using the framework of higher category theory, we introduce appropriate 2-groups and 3-groups, and construct the actions for the corresponding constrained 2BF and 3BF theories. In this way, we can construct actions which describe the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl, and Majorana fields coupled to Einstein-Cartan gravity. Each action is naturally split into a topological sector and a sector with simplicity constraints. The properties of the higher gauge group structure opens up a possibility of a nontrivial unification of all fields.
