We study higher-form symmetries and a higher group in the low energy limit of a $(3+1)$-dimensional axion electrodynamics with a massive axion and a massive photon. A topological field theory describing topological excitations with the axion-photon coupling, which we call a topological axion electrodynamics, is obtained in the low energy limit. Higher-form symmetries of the topological axion electrodynamics are specified by equations of motion and Bianchi identities. We find that there are induced anyons on the intersections of symmetry generators. By a link of worldlines of the anyons, we show that the worldvolume of an axionic domain wall is topologically ordered. We further specify the underlying mathematical structure elegantly describing all salient features of the theory to be a 4-group.

我们在低能量极限中研究更高形式的对称性和更高的群 $(3+1)$具有大质量轴子和大质量光子的 维轴子电动力学。在低能量极限下获得了描述具有轴子-光子耦合的拓扑激发的拓扑场理论，我们称之为拓扑轴子电动力学。拓扑轴子电动力学的高级对称性由运动方程和 Bianchi 恒等式指定。我们发现在对称发生器的交点上存在诱导任意子。通过任意子的世界线链接，我们表明轴子畴壁的世界体积是拓扑有序的。我们进一步指定了潜在的数学结构，优雅地将理论的所有显着特征描述为 4 组。