论文标题
$ e $ -manifolds的古典仪表理论的汉密尔顿
Hamiltonian facets of classical gauge theories on $E$-manifolds
论文作者
论文摘要
带有边界的歧管，有角落，$ b $ - manifolds和叶子模型配置空间，用于在约束下移动的粒子，可以描述为$ e $ -Manifolds。 $ e $ - manifolds是在[NT01]中引入的，并在[MS20]中进行了深入研究。在本文中，我们通过将规格理论扩展到$ e $类别来探讨它们的物理方面。可以在几种新场景中描述经典粒子的配置空间中的奇异性，以$ e $ sy-symplectic歧管揭示其哈密顿的方面。遵循[WEI78]在[WEI78]中启用的方案之后，我们显示了与$ e $ gouge场相互作用的粒子的通用模型的存在。此外，我们将杨米尔斯理论中相位空间的描述概括为泊松歧管及其最小耦合过程，如[MON86]中所示，对于具有$ e $结构的基本歧管。特别是，在Coadhexhight Orbits和转移技巧上的减少扩展到了此框架。我们表明，黄色方程描述了粒子与阳米尔斯领域的相互作用，在$ e $ setting中成为哈密顿量。我们在Minkowski空间中制定了电磁量表，该空间与适当的时间叶叶相关，我们看到我们的主要定理描述了物理模型（例如压实的黑洞）中的最小耦合。
Manifolds with boundary, with corners, $b$-manifolds and foliations model configuration spaces for particles moving under constraints and can be described as $E$-manifolds. $E$-manifolds were introduced in [NT01] and investigated in depth in [MS20]. In this article we explore their physical facets by extending gauge theories to the $E$-category. Singularities in the configuration space of a classical particle can be described in several new scenarios unveiling their Hamiltonian aspects on an $E$-symplectic manifold. Following the scheme inaugurated in [Wei78], we show the existence of a universal model for a particle interacting with an $E$-gauge field. In addition, we generalize the description of phase spaces in Yang-Mills theory as Poisson manifolds and their minimal coupling procedure, as shown in [Mon86], for base manifolds endowed with an $E$-structure. In particular, the reduction at coadjoint orbits and the shifting trick are extended to this framework. We show that Wong's equations, which describe the interaction of a particle with a Yang-Mills field, become Hamiltonian in the $E$-setting. We formulate the electromagnetic gauge in a Minkowski space relating it to the proper time foliation and we see that our main theorem describes the minimal coupling in physical models such as the compactified black hole.
