Anyon wave equations and the noncommutative plane
Peter A. Horvathy, Mikhail S. Plyushchay
TL;DR
This paper derives infinite-component wave equations for exotic particles in a noncommutative plane, revealing a new representation of the Galilei group and analyzing the velocity operator and coordinates.
Contribution
It introduces a novel infinite-component wave equation framework for anyons in a noncommutative setting, linked to the two-fold central extension of the planar Galilei group.
Findings
Identifies an infinite-dimensional representation of the Galilei group.
Analyzes the velocity operator for exotic particles.
Defines observable coordinates on a noncommutative plane.
Abstract
The ``Jackiw-Nair'' non-relativistic limit of the relativistic anyon equations provides us with infinite-component wave equations of the Dirac-Majorana-Levy-Leblond type for the ``exotic'' particle, associated with the two-fold central extension of the planar Galilei group. An infinite dimensional representation of the Galilei group is found. The velocity operator is studied, and the observable coordinates describing a noncommutative plane are identified.
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