Gauge-invariant magnetic translation operators, built from a gauge-covariant pseudo-momentum P, reproduce Curtright-Zachos generators through a rotation-dilatation duality.
Electric Space-time Translation and Floquet-Bloch Wavefunction
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abstract
As for the study of Landau level wavefunctions for the quantum Hall effect, the magnetic Bloch wavefunctions based on the magnetic translation symmetry have been extensively investigated in the past few decades. In this article, the electric Floquet-Bloch wavefunctions based on the electric translation symmetry are studied as well as the momentum-frequency Brillouin zone, which is applied to the problem of one dimensional tight-binding model under an external electric field. The spectrum of electric Floquet-Bloch states can be generated by the projective representation of electric translation group, and the topological properties of these states are investigated.
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Gauge Invariant and Generic Formulation of Magnetic Translations and so(3,1) Curtright-Zachos Generators
Gauge-invariant magnetic translation operators, built from a gauge-covariant pseudo-momentum P, reproduce Curtright-Zachos generators through a rotation-dilatation duality.