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An extended Galilei group and its application

O. Holmaas

International Journal of Theoretical PhysicsMay 1, 19710 citations

Representations of the Galilei Group

Erdal İnönü, E. P. Wigner

Springer eBooksJan 1, 19930 citations

Representations of the Galilei group

Erdal İnönü, Eugene Paul Wigner

Il Nuovo CimentoAug 1, 1952180 citations

Galilei group and Liouville equation

A. Loinger

Annals of PhysicsOct 1, 196224 citations

The "Peierls substitution" and the exotic Galilei group

Christian Duval, P. A. Horváthy

Owing to the two-parameter central extension of the planar Galilei group, anon relativistic particle in the plane admits an extra structure, which yieldsnoncommuting coordinates. For a particle moving in a magnetic fieldperpendicular to the plane, the two parameters combine with the magnetic fieldto provide an effective mass. For vanishing effective mass the phase spaceadmits a two-dimensional reduction, which represents the condensation tocollective ``Hall'' motions and justifies the rule called ``Peierlssubstitution''. Then Geometric Quantization yields the wave functions proposedby Laughlin to describe the Fractional Quantum Hall Effect.Owing to the two-parameter central extension of the planar Galilei group, anon relativistic particle in the plane admits an extra structure, which yieldsnoncommuting coordinates. For a particle moving in a magnetic fieldperpendicular to the plane, the two parameters combine with the magnetic fieldto provide an effective mass. For vanishing effective mass the phase spaceadmits a two-dimensional reduction, which represents the condensation tocollective ``Hall'' motions and justifies the rule called ``Peierlssubstitution''. Then Geometric Quantization yields the wave functions proposedby Laughlin to describe the Fractional Quantum Hall Effect.

Feb 28, 200036 citations

The exotic Galilei group and

Christian Duval, Parc de Grandmont

Taking advantage of the two-parameter central extension of the planar Galilei group, we construct a non relativistic particle model in the plane. Owing to the extra structure, the coordinates do not commute. Our model can be viewed as the non-relativistic counterpart of the relativistic anyon considered before by Jackiw and Nair. For a particle moving in a magnetic field perpendicular to the plane, the two parameters combine with the magnetic field to provide an effective mass. For vanishing effective mass the phase space admits a two-dimensional reduction, which represents the condensation to collective “Hall” motions, and justifies the rule called “Peierls substitution”. Quantization yields the wave functions proposed by Laughlin to describe the Fractional Quantum Hall Effect.Taking advantage of the two-parameter central extension of the planar Galilei group, we construct a non relativistic particle model in the plane. Owing to the extra structure, the coordinates do not commute. Our model can be viewed as the non-relativistic counterpart of the relativistic anyon considered before by Jackiw and Nair. For a particle moving in a magnetic field perpendicular to the plane, the two parameters combine with the magnetic field to provide an effective mass. For vanishing effective mass the phase space admits a two-dimensional reduction, which represents the condensation to collective “Hall” motions, and justifies the rule called “Peierls substitution”. Quantization yields the wave functions proposed by Laughlin to describe the Fractional Quantum Hall Effect.

Jan 1, 20081 citation

The exotic Galilei group and the “Peierls substitution”

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