Exotic Carroll particles with two-parameter central extension move by an anomalous Hall law, and their critical reduction reproduces the Dunne-Jackiw-Trugenberger model underlying the Peierls substitution.
Noncommutative Phase Spaces by Coadjoint Orbits Method
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abstract
We introduce noncommutative phase spaces by minimal couplings (usual one, dual one and their mixing). We then realize some of them as coadjoint orbits of the anisotropic Newton-Hooke groups in two- and three-dimensional spaces. Through these constructions the positions and the momenta of the phase spaces do not commute due to the presence of a magnetic field and a dual magnetic field.
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Peierls substitution and Hall motion in exotic Carroll dynamics
Exotic Carroll particles with two-parameter central extension move by an anomalous Hall law, and their critical reduction reproduces the Dunne-Jackiw-Trugenberger model underlying the Peierls substitution.