论文标题
在存在边界的情况下对现场理论的规范分析：麦克斯韦+pontryagin
Canonical analysis of field theories in the presence of boundaries: Maxwell+Pontryagin
论文作者
论文摘要
我们研究了在边界存在下对仪表理论的规范分析。尽管Regge和Teitelboim提出的界限在存在边界的情况下实施了Dirac计划并不是什么新鲜事，但在某些情况下，这种形式主义是不完整的。在这里，我们提出了与dirac形式主义的扩展 - 与regge-teitelboim策略 - 包括一般的野外理论案例。我们看到有两种可能的场景，一个场景没有边界对符号结构的贡献，另一个情况下有一个情况，其中一种情况，取决于起始动作原理的动态细节。作为一个示例这两种情况的具体系统，我们认为可以将一种理论视为在具有边界的四维时空区域上定义的理论，该区域具有边界 - 批量理论 - 或在该地区的批量和边界上既定义的理论 - 混合理论 - 混合理论 - 。批量理论由4维Maxwell + $ U（1）$ pontryagin Action给出，而混合的动作是由4维Maxwell + 3维$ U（1）$ Chern-Simons在边界上定义的。最后，我们展示了如何通过提供第三个描述的规范转换来连接同一系统的这两个描述。这里的重点是定义所有三个描述的一致表述，为此，我们依赖于受约束系统的几何公式，以及在手稿中提出的Dirac-Regge-teitelboim（DRT）形式主义的扩展。
We study the canonical Hamiltonian analysis of gauge theories in the presence of boundaries. While the implementation of Dirac's program in the presence of boundaries, as put forward by Regge and Teitelboim, is not new, there are some instances in which this formalism is incomplete. Here we propose an extension to the Dirac formalism --together with the Regge-Teitelboim strategy,-- that includes generic cases of field theories. We see that there are two possible scenarios, one where there is no contribution from the boundary to the symplectic structure and the other case in which there is one, depending on the dynamical details of the starting action principle. As a concrete system that exemplifies both cases, we consider a theory that can be seen both as defined on a four dimensional spacetime region with boundaries --the bulk theory--, or as a theory defined both on the bulk and the boundary of the region --the mixed theory--. The bulk theory is given by the 4-dimensional Maxwell + $U(1)$ Pontryagin action while the mixed one is defined by the 4-dimensional Maxwell + 3-dimensional $U(1)$ Chern-Simons action on the boundary. Finally, we show how these two descriptions of the same system are connected through a canonical transformation that provides a third description. The focus here is in defining a consistent formulation of all three descriptions, for which we rely on the geometric formulation of constrained systems, together with the extension of the Dirac-Regge-Teitelboim (DRT) formalism put forward in the manuscript.
