We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine structure constant is rational, the theory admits noninvertible symmetries which can be realized as composites of electric-magnetic duality and gauging a discrete subgroup of the one-form global symmetry. These noninvertible symmetries are approximate quantum invariances of the natural world which emerge in the infrared below the mass scale of charged particles. We construct these symmetries explicitly as topological defects and illustrate their action on local and extended operators. We also describe their action on boundary conditions and illustrate some consequences of the symmetry for Hilbert spaces of the theory defined in finite volume.

中文翻译：

---

电磁学中的量子二象性和精细结构常数

我们描述了麦克斯韦理论中的电磁二象性和更高对称性之间的相互作用。当精细结构常数是有理数时，该理论承认不可逆对称性，这种对称性可以作为电磁对偶性的复合体来实现，并测量一式全局对称性的离散子群。这些不可逆对称性是自然界中近似的量子不变性，它们出现在带电粒子质量尺度以下的红外光中。我们将这些对称性明确地构造为拓扑缺陷，并说明它们对局部和扩展算子的作用。我们还描述了它们对边界条件的作用，并说明了有限体积中定义的理论希尔伯特空间的对称性的一些结果。