标题： 卡洛尔动力学中的霍尔效应 显示英文标题

标题： Hall effects in Carroll dynamics

摘要： “卡罗尔粒子会移动吗？” 答案取决于粒子的特性，如其质量、自旋、电荷和磁矩。 一个具有质量的卡罗尔粒子（与分形子密切相关）不会移动；其静止性来源于卡罗尔提升对称性，该对称性意味着偶极子守恒，但反之则不成立。 无质量的卡罗尔粒子可能通过遵循霍尔定律传播，这与卡罗尔提升对称性的部分破坏一致。 该框架被扩展到卡罗尔场论。 在$d=2$空间维度中，卡罗尔群有一个二重中心扩张，这使我们能够将动力学推广到有质量和无质量粒子，包括任意子。 任意子的自旋和磁矩与由两个卡西米尔不变量参数化的双重扩张结构结合，这两个卡西米尔不变量被解释为固有磁化强度和非对易性参数。 受电磁背景场影响的扩展卡罗尔粒子按照广义霍尔定律运动，该定律包括塞曼力。 该理论通过我们称为奇异光子的无质量、电中性任意子来说明，这些任意子具有双重中心扩张结构，在黑洞的视界上运动，产生任意子自旋霍尔效应。 显示英文摘要

摘要： ``Do Carroll particles move?'' The answer depends on the characteristics of the particle such as its mass, spin, electric charge, and magnetic moment. A massive Carroll particle (closely related to fractons) does not move; its immobility follows from Carroll boost symmetry which implies dipole conservation, but not conversely. A massless Carroll particle may propagate by following the Hall law, consistently with the partial breaking of the Carroll boost symmetry. The framework is extended to Carroll field theory. In $d=2$ space dimensions, the Carroll group has a two-fold central extension which allows us to generalize the dynamics to massive and massless particles, including anyons. The anyonic spin and magnetic moment combine with the doubly-extended structure parameterized by two Casimir invariants interpreted as intrinsic magnetization and non-commutativity parameter. The extended Carroll particle subjected to an electromagnetic background field moves following a generalized Hall law which includes a Zeeman force. This theory is illustrated by massless, uncharged anyons with doubly-centrally extended structure we call exotic photons, which move on the horizon of a Black Hole, giving rise to an anyonic spin-Hall Effect.