Electrons in solids constitute quantum many-body systems showing a variety of phenomena. It often happens that the eigen states of the Hamiltonian are classified into subgroups separated by energy gaps. Band structures in solids and spin polarization in Mott insulators are two representative examples. The subspace spanned by these wavefunctions belonging to each of this subgroup can be regarded as a manifold in Hilbert space, and concepts concerning differential geometry become relevant. Connection and curvature are two key quantities, which correspond to the vector potential and field strength of electromagnetism, respectively. Therefore, one can construct an effective electromagnetic field from the structure of the Hilbert space, which is called an "emergent electromagnetic field". In this article, we review the physics related to this emergent electromagnetic field in solids, including the gauge theory of strongly correlated electrons, various Hall effects, multiferroics, topological matter, magnetic texture such as skyrmions, and the shift current in noncentrosymmetric materials.

中文翻译：

---

凝聚态中的新兴电磁现象。

固体中的电子构成了显示多种现象的量子多体系统。经常发生的是，哈密顿量的本征态被能隙分隔为子组。固体中的能带结构和莫特绝缘子中的自旋极化是两个代表性的例子。这些属于每个子组的波函数所跨越的子空间可以视为希尔伯特空间中的流形，有关微分几何的概念也变得很重要。连接和曲率是两个关键量，分别对应于矢量势和电磁场强度。因此，可以从希尔伯特空间的结构中构造出有效的电磁场，称为“紧急电磁场”。在这篇文章中，