论文标题
减少协变田理论
Gauge reduction in covariant field theory
论文作者
论文摘要
在这项工作中，我们开发了具有仪表对称性的协方差理论的拉格朗日还原理论。这些对称性是由在配置束上作用光纤的Lie组纤维束建模的。为了减少变分原理，我们利用了广义主连接，这是一种由光纤动作等效化的Ehresmann连接。获得还原方程后，我们给出了重建条件，并将垂直还原方程与Noether定理联系起来。最后，我们用几个示例说明了理论，包括经典案例（Lagrange-Poincaré降低），电磁主义，破坏对称性和非亚洲仪表理论。
In this work, we develop a Lagrangian reduction theory for covariant field theories with gauge symmetries. These symmetries are modeled by a Lie group fiber bundle acting fiberwisely on a configuration bundle. In order to reduce the variational principle, we utilize generalized principal connections, a type of Ehresmann connections that are equivariant by the fiberwise action. After obtaining the reduced equations, we give the reconstruction condition and we relate the vertical reduced equation with the Noether theorem. Lastly, we illustrate the theory with several examples, including the classical case (Lagrange-Poincaré reduction), Electromagnetism, symmetry-breaking and non-Abelian gauge theories.
