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arXiv · 2212.02360

Hall effects in Carroll dynamics

L. Marsot·P. -M. Zhang·M. Chernodub·P. A. Horvathy
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Abstract

``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.

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L. Marsot, P. -M. Zhang, M. Chernodub, P. A. Horvathy. 2022-12-05. Hall effects in Carroll dynamics. https://doi.org/10.1016/j.physrep.2023.07.007

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