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arXiv · 2608.29931

Carrollian Wave Equations for Arbitrary Spin: Anyons and the Exotic Particle on the Noncommutative Plane

Mauricio Valenzuela
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Abstract

We construct the Carrollian limit of the Cort\'es--Plyushchay wave equations for planar anyons, grading the spin-tower components by powers of $c$ and taking the limit at fixed rest energy. The result is a linear system describing Carrollian particles of any real spin --- \emph{Carrollian anyons} --- and, at (half-)integer spin, Carrollian bosons, fermions and higher-spin fields. The system is a first-order square root of the standard Carroll wave equation $(\partial_t^2+E^2)\Phi=0$, whose spectrum consists of two flat branches at plus and minus the rest energy. Scaling the spin along with $c$, in the Carrollian analogue of the Jackiw--Nair limit, yields instead the exotic Carroll algebra, with a second central charge, non-commuting boosts, and observable coordinates spanning a noncommutative plane. We show how the Galilean and Carrollian theories branch from one common similarity transformation: the Galilean limit expels the negative-energy modes, whereas the Carroll limit retains both relativistic branches.

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Mauricio Valenzuela. 2026-08-30. Carrollian Wave Equations for Arbitrary Spin: Anyons and the Exotic Particle on the Noncommutative Plane. https://arxiv.org/abs/2608.29931

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