Non-commutative mechanics, in mathematical & in condensed matter physics

Details Non-commutative mechanics, in mathematical & in condensed matter physics Non-commutative mechanics, in mathematical & in condensed matter physics

2006-09-22

arxiv.org/abs/cond-mat/0609571v2

SIGMA 2 (2006), 090, 9 pages

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (

Scientific paper

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.

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