电磁学作为一种突现现象：逐步指南
Electromagnetism as an emergent phenomenon: a step-by-step guide
摘要：
我们给出了详细的描述电动力学作为一个新兴的理论，从凝聚物质的结构，不仅{ \it本身}，但也作为一个热身的研究更复杂的情况下，重力。我们将集中讨论两种情况，尽管性质不同，但它们有一些共同的重要特征，我们的想法是提取产生涌现电动力学和更一般的规范理论的基本一般成分。我们从麦克斯韦的电动力学模型开始，麦克斯韦方程组作为动力学一致性条件出现。接下来，我们将超流$^3$类氦系统作为一类广泛的费米子量子系统的代表，它们的低能物理学再现了经典电动力学（狄拉克和麦克斯韦方程组作为动力学低能定律）。从这两种分析中可以得出的一个重要教训是，矢量势具有微观物理实在性，只有在低能区，这种物理实在性才变得模糊，有利于规范不变性，而规范不变性又被证明是仅次于有效洛伦兹不变性的。
英文摘要：
We give a detailed description of electrodynamics as an emergent theory from condensed-matter-like structures, not only {\it per se} but also as a warm-up for the study of the much more complex case of gravity. We will concentrate on two scenarios that, although qualitatively different, share some important features, with the idea of extracting the basic generic ingredients that give rise to emergent electrodynamics and, more generally, to gauge theories. We start with Maxwell's mechanical model for electrodynamics, where Maxwell's equations appear as dynamical consistency conditions. We next take a superfluid $^3$He-like system as representative of a broad class of fermionic quantum systems whose low-energy physics reproduces classical electrodynamics (Dirac and Maxwell equations as dynamical low-energy laws). An important lesson that can be derived from both analyses is that the vector potential has a microscopic physical reality and that it is only in the low-energy regime that this physical reality is blurred in favour of gauge invariance, which in addition turns out to be secondary to effective Lorentz invariance.
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