论文标题
Yang-Mills理论的符合性降低具有边界：从超选择部门到边缘模式，再到后面
Symplectic reduction of Yang-Mills theory with boundaries: from superselection sectors to edge modes, and back
论文作者
论文摘要
我开发了一种符合性还原理论，该理论适用于杨米尔斯理论和电磁学中的有限区域。在该理论中，通过该地区边界的电通量量规范的超选择扇区起着核心作用：在此类扇区中，存在一个自然的，规范定义的，符合性的结构，用于降低的阳米尔斯理论。这种符合性结构不需要包含任何新的自由度。在非亚洲案件中，它还支持了一个汉密尔顿矢量场的家族，我称之为“通量旋转”，这是由涂抹的，泊松 - 非交通型的电气通量产生的。由于通量旋转的作用会影响系统的总能量，因此我认为通量旋转并不是仅限于一个区域的Yang-Mills理论的动态对称性。我还考虑了在所有超选择部门的结合上定义象征结构的可能性。反过来，这需要包括额外的边界自由度又称“边缘模式”。但是，除非新的边缘模式模型位于该区域边界的材料物理系统，否则我认为，边缘模式的相空间扩展本质上是模棱两可的，量规破坏。
I develop a theory of symplectic reduction that applies to bounded regions in Yang-Mills theory and electromagnetism. In this theory gauge-covariant superselection sectors for the electric flux through the boundary of the region play a central role: within such sectors, there exists a natural, canonically defined, symplectic structure for the reduced Yang-Mills theory. This symplectic structure does not require the inclusion of any new degrees of freedom. In the non-Abelian case, it also supports a family of Hamiltonian vector fields, which I call "flux rotations," generated by smeared, Poisson-non-commutative, electric fluxes. Since the action of flux rotations affects the total energy of the system, I argue that flux rotations fail to be dynamical symmetries of Yang-Mills theory restricted to a region. I also consider the possibility of defining a symplectic structure on the union of all superselection sectors. This in turn requires including additional boundary degrees of freedom aka "edge modes." However, unless the new edge modes model a material physical system located at the boundary of the region, I argue that the phase space extension by edge modes is inherently ambiguous and gauge-breaking.
