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Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics

Alain Berard·Herve Mohrbach
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Abstract

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.

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Alain Berard, Herve Mohrbach. 2004-04-14. Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics. https://doi.org/10.1103/physrevd.69.127701

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