论文标题
Tulczyjew三重仪表田理论
The Tulczyjew triple for gauge field theories
论文作者
论文摘要
在本文中，我们构建并讨论了针对仪表田理论的新的严格几何形式主义。我们作品的基础是Tulczyjew Triple的概念，Tulczyjew Triple是一种几何结构，在力学和经典领域理论的数学描述中成功解决了许多问题。特别是，我们为量规场理论构建了一个Tulczyjew三重，并将其减少仅取决于连接和曲率值的系统，而不是量规场的整个第一架。我们还介绍了新的几何结构，例如捆绑包的矢量仿物产品，并从新的角度分析了连接捆绑包。最后，我们将衍生的形式主义应用于杨米尔斯理论。
In this article we construct and discuss a new rigorous geometric formalism for gauge field theories. The basis of our work is the notion of the Tulczyjew triple, a geometric structure which successfully solved numerous problems in mathematical description of mechanics and classical field theory. In particular, we construct a Tulczyjew triple for gauge field theories and reduce it for systems that depend only on the value of a connection and curvature instead of the entire first jet of the gauge field. We also introduce new geometric structures such as the vector-affine product of bundles and analyse the connection bundle from a new perspective. Finally, we apply the derived formalism to Yang-Mills theory.
