2003/10/31 by Alain Berard, Herve Mohrbach · 2 citations
Physics and Astronomy · #hep-th #cond-mat
paper · pdf · doi:10.1103/physrevd.69.127701
published as Phys.Rev. D69 (2004) 127701 · 4 pages
arxiv created 2004/04/14 · arxiv updated 2009/12/01
To build genuine generators of the rotations group in noncommutative quantum mechanics, we show that it is necessary to extend the noncommutative parameter θ to a field operator, which one proves to be only momentum dependent. We find consequently that this field must be obligatorily a dual Dirac monopole in momentum space. Recent experiments in the context of the anomalous Hall effect provide for a monopole in the crystal momentum space. We suggest a connection between the noncommutative field and the Berry curvature in momentum space which is at the origine of the anomalous Hall effect.