论文标题
深红色的量规理论的经典动力学
The classical dynamics of gauge theories in the deep infrared
论文作者
论文摘要
渐近平面设置中的量规和重力理论具有无限的许多保守电荷，与无限无限的大型仪表转换或差异性相关。这些指控在多大程度上限制了这些理论中的散射？在文献中据称，由于硬和软扇区的脱钩，保守的电荷仅限制了软扇区中的动力学，因此约束是微不足道的。我们表明，由于具有有限维度的符号几何形状的属性的无限维度的失败，因此该解耦的论点失败了。专门针对四维Minkowski时空的无质量电荷标量场耦合到无质量的标量场，我们明确地表明，这两个扇区始终使用散射图的扰动经典计算来耦合。具体而言，虽然这两个扇区以低订单未耦合，但它们通过电磁记忆效应以四分之一的顺序耦合。无法通过调整硬和软扇区的定义来消除这种耦合（其中包括打扮硬度自由度的经典类似物）。我们得出的结论是，保守的费用对硬度自由度的散射产生了非平凡的约束。该结论也应适用于重力散射以及黑洞的形成和蒸发。 在开发经典散射理论时，我们表明，通用的洛伦兹量规解决方案无法满足Strominger提出的空间无穷大的矢量潜力的匹配条件来定义现场配置空间，我们建议一种解决此问题的方法。我们还表明，当存在柔软的自由度时，在洛伦兹仪表中，在散射图中首次出现非线性的顺序是二阶，但在其他仪表中可以是第三阶。
Gauge and gravitational theories in asymptotically flat settings possess infinitely many conserved charges associated with large gauge transformations or diffeomorphisms that are nontrivial at infinity. To what extent do these charges constrain the scattering in these theories? It has been claimed in the literature that the constraints are trivial, due to a decoupling of hard and soft sectors for which the conserved charges constrain only the dynamics in the soft sector. We show that the argument for this decoupling fails due to the failure in infinite dimensions of a property of symplectic geometry which holds in finite dimensions. Specializing to electromagnetism coupled to a massless charged scalar field in four dimensional Minkowski spacetime, we show explicitly that the two sectors are always coupled using a perturbative classical computation of the scattering map. Specifically, while the two sectors are uncoupled at low orders, they are coupled at quartic order via the electromagnetic memory effect. This coupling cannot be removed by adjusting the definitions of the hard and soft sectors (which includes the classical analog of dressing the hard degrees of freedom). We conclude that the conserved charges yield nontrivial constraints on the scattering of hard degrees of freedom. This conclusion should also apply to gravitational scattering and to black hole formation and evaporation. In developing the classical scattering theory, we show that generic Lorenz gauge solutions fail to satisfy the matching condition on the vector potential at spatial infinity proposed by Strominger to define the field configuration space, and we suggest a way to remedy this. We also show that when soft degrees of freedom are present, the order at which nonlinearities first arise in the scattering map is second order in Lorenz gauge, but can be third order in other gauges.
