Non-commutative mechanics, in mathematical & in condensed matter physics
Abstract
Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table~1). Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ``exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.
Keywords
Cite
@article{arxiv.cond-mat/0609571,
title = {Non-commutative mechanics, in mathematical & in condensed matter physics},
author = {P. A. Horvathy},
journal= {arXiv preprint arXiv:cond-mat/0609571},
year = {2007}
}
Comments
This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/