论文标题
在边界上构建理论，其动力和自由度
Constructing the theory at the boundary, its dynamics and degrees of freedom
论文作者
论文摘要
鉴于由拉格朗日定义的时空区域中的理论，我们提出了一种在边界处找到相应理论的方法（无论是空间状的还是时间样），这使我们能够识别边界上的自由度，而无需确定任何规范的固定或进一步的假设。我们首先在边界找到相应的动作原理。从中，我们可以找到相应的运动方程，边界的自由度和自由度。然后，我们表征边界的自由度。我们通过分析经过广泛研究的三维Abelian Chern-Simons理论来体现这种方法。我们通过汉密尔顿框架发现，边界理论具有一种自由度，可以用手性玻色子来表征：量子厅边缘模式。我们还发现，具有边界条件的量规固定之间的对应关系，并讨论这是否足以具有良好的动作原理和可能的情况。
Given a theory in a region of space-time with boundaries, defined by a Lagrangian, we propose a method to find the corresponding theory at the boundary (either space-like or time-like), that allows us to identify the degrees of freedom at the boundary without any gauge fixing nor further assumptions a priori. We start by finding the corresponding action principle at the boundary. From this, we can find the corresponding equations of motion, the symmetries and degrees of freedom at the boundary. Then we characterise the degrees of freedom at the boundary. We exemplify this method by analysing the broadly studied 3-dimensional Abelian Chern-Simons theory. We found, through the Hamiltonian framework, that the boundary theory has one degree of freedom that can be characterised by the chiral boson: the Quantum Hall edge modes. We also find a correspondence between a gauge fixing in the bulk with a boundary condition and discuss whether this is enough to have a well-posed action principle and the possible scenarios.
