Anyon wave equations and the noncommutative plane
Résumé
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.