论文标题
连接空间的捆绑几何形状，协变汉密顿形式主义，量规理论中的边界问题和梳妆场方法
Bundle geometry of the connection space, covariant Hamiltonian formalism, the problem of boundaries in gauge theories, and the dressing field method
论文作者
论文摘要
我们利用了连接空间的主要束几何形状，以获得两类（纯）仪表理论的两类的预成成结构的一般结果：不变理论和满足两个限制假设的不变理论。特别是，在两种情况下，我们都会得出预成型电势和预成成2形式的一般场依赖性仪表变换。我们指出，标准束几何形状的概括（称为扭曲的几何形状）自然出现在非变变仪表理论的研究中（例如非亚伯利亚的Chern-Simons理论）。这些结果证明，将符号结构与有限区域相关的量规理论的众所周知的问题是两个类别的一般特征。最近引入的边缘模式策略是在各种情况下在各种情况下积极开发的。我们将注意力框架作为几何框架或涵盖该策略的基础。该方法提供的几何见解既阐明它，又清楚地描述了其潜在的缺点以及成功条件。将我们的一般框架应用于各种示例，可以直接恢复边缘模式和一般相对性的预成立结构的最新文献的几个结果。
We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories, and non-invariant theories satisfying two restricting hypothesis. In particular, we derive the general field-dependent gauge transformations of the presymplectic potential and presymplectic 2-form in both cases. We point-out that a generalisation of the standard bundle geometry, called twisted geometry, arises naturally in the study of non-invariant gauge theories (e.g. non-Abelian Chern-Simons theory). These results prove that the well-known problem of associating a symplectic structure to a gauge theory over bounded regions is a generic feature of both classes. The edge modes strategy, recently introduced to address this issue, has been actively developed in various contexts by several authors. We draw attention to the dressing field method as the geometric framework underpinning, or rather encompassing, this strategy. The geometric insight afforded by the method both clarifies it and clearly delineates its potential shortcomings as well as its conditions of success. Applying our general framework to various examples allows to straightforwardly recover several results of the recent literature on edge modes and on the presymplectic structure of general relativity.
