Carrollian Wave Equations for Arbitrary Spin: Anyons and the Exotic Particle on the Noncommutative Plane
Abstract
We construct the Carrollian limit of the Cortés--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 (∂t2+E2)Φ=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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BibTeX
@misc{valenzuela2026carrollian,
title = {{Carrollian Wave Equations for Arbitrary Spin: Anyons and the Exotic Particle on the Noncommutative Plane}},
author = {Mauricio Valenzuela},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29931},
eprint = {2608.29931},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29931},
}
RIS
TY - UNPB
TI - Carrollian Wave Equations for Arbitrary Spin: Anyons and the Exotic Particle on the Noncommutative Plane
AU - Mauricio Valenzuela
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29931
UR - https://arxiv.org/abs/2608.29931
AB - We construct the Carrollian limit of the Cortés--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 (∂_t^2+E^2)Φ=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.
ER -