Non-Commutative Mechanics in Mathematical in Condensed Matter Physics

Peter A. Horváthy

Symmetry, integrability and geometry: methods and applications, Tome 2 (2006)

Résumé

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.

Détail

Keywords: non-commutative mechanics; semiclassical models; Hall effect.

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