The exotic Galilei group and the “ Peierls substitution

@inproceedings{Thorique2008TheEG,
  title={The exotic Galilei group and the “ Peierls substitution},
  author={C. Duval Centre de Physique Th{\'e}orique and P{\'e}ter A. Horvathy},
  year={2008}
}
Taking advantage of the two-parameter central extension of the planar Galilei group, we construct a non relativistic particle model in the plane. Owing to the extra structure, the coordinates do not commute. Our model can be viewed as the non-relativistic counterpart of the relativistic anyon considered before by Jackiw and Nair. For a particle moving in a magnetic field perpendicular to the plane, the two parameters combine with the magnetic field to provide an effective mass. For vanishing… CONTINUE READING