场空间边界的测量
Gauging the Boundary in Field-space
摘要：
定域规范理论与边界有着复杂的关系。固定量规通常可以消除不必要的冗余，而不同边界区域的耦合则需要使用量规可变元件。因此，正如通常理解的那样，耦合不利于量规固定。这种推理导致一些人宣称子系统的耦合是规范存在的理由。事实上，虽然规范固定是完全没有问题的一个单一的区域没有边界，它引入了任意的边界条件的规范自由度本身-这些条件缺乏物理解释时，他们不是原来的领域的泛函。这种任意的边界选择会渗透到通过诺特第二定理计算电荷的过程中，混淆了物理电荷与局域规范对称性的关系。由规范在边界上造成的混乱是众所周知的，必须在概念上和技术上加以解决。在这里，我解释了上述问题，并说明了一个可能的解决方案：在最近的一系列文件的概念，一个连接形式的提出和实施的领域空间的规范理论。利用这一工具，辛几何的一个修改版本-称为“水平”-是可能的。独立于边界条件，这种形式主义赋予每个区域一个物理上突出的、相关的电荷概念：水平诺特电荷。与此同时，根据需要，连接形式调解了区域的和平组成，这与每个区域的水平Noether电荷的归属是相容的。
英文摘要：
Local gauge theories are in a complicated relationship with boundaries. Whereas fixing the gauge can often shave off unwanted redundancies, the coupling of different bounded regions requires the use of gauge-variant elements. Therefore, coupling is inimical to gauge-fixing, as usually understood. This sort of reasoning has led some to declare the coupling of subsystems to be the raison d'être of gauge. Indeed, while gauge-fixing is entirely unproblematic for a single region without boundary, it introduces arbitrary boundary conditions on the gauge degrees of freedom themselves -- these conditions lack a physical interpretation when they are not functionals of the original fields. Such arbitrary boundary choices creep into the calculation of charges through Noether's second theorem, muddling the assignment of physical charges to local gauge symmetries. The confusion brewn by gauge at boundaries is well-known, and must be contended with both conceptually and technically. Here I explicate the problems mentioned above and illustrate a possible resolution: in a recent series of papers the notion of a connection-form was put forward and implemented in the field-space of gauge theories. Using this tool, a modified version of symplectic geometry -- called `horizontal' -- is possible. Independently of boundary conditions, this formalism bestows to each region a physically salient, relational notion of charge: the horizontal Noether charge. Meanwhile, as required, the connection-form mediates a peaceful composition of regions, one compatible with the attribution of horizontal Noether charges to each region.
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