Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics

Details Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics

2003-10-17

arxiv.org/abs/hep-th/0310167v3

Phys.Rev. D69 (2004) 127701

Physics

High Energy Physics

High Energy Physics - Theory

4 pages

Scientific paper

10.1103/PhysRevD.69.127701

To build genuine generators of the rotations group in noncommutative quantum mechanics, we show that it is necessary to extend the noncommutative parameter $\theta $ 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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