标题： 平面及其Carroll-Galilei对称性 显示英文标题

标题： Planons and their Carroll-Galilei symmetries

摘要： 我们通过共伴随轨道和中心扩张平面子群的酉不可约表示对平面子进行分类，研究了平面子的动力学，这些粒子的运动受限于一个平面。 平面子与伽利略/巴格曼对称性密切相关，值得注意的是，通常被忽视的伽利略群的质量为零的共伴随轨道在其描述中起着核心作用。 因此，我们为这些轨道提供了非平凡的物理解释。 我们进一步将经典和量子偶极子构造为单极子的束缚态，其中受限的平面运动来自于一种新颖的混合卡罗尔-伽利略对称性。 我们还指出，具有卡罗尔对称性的最简单且已实验实现的系统存在于晶体中。 显示英文摘要

摘要： We study the dynamics of planons, particles whose mobility is restricted to a plane, through the classification of coadjoint orbits and unitary irreducible representations of the centrally extended planon group. Planons are closely related to Galilei/Bargmann symmetries and, remarkably, the often-ignored massless coadjoint orbits of the Galilei group play a central r\^ole in their description. We thereby provide a nontrivial physical interpretation of these orbits. We further construct classical and quantum dipoles as bound states of monopoles, where the restricted planar motion arises from a novel mixed Carroll-Galilei symmetry. We also argue that the simplest and already experimentally realised systems with Carroll symmetry are in crystals.