Kohn's theorem, Larmor's equivalence principle and the Newton-Hooke group
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We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a " relativity group" which is a one-parameter family of deformations of the standard Galilei group to the Newton-Hooke group which is a Wigner-nn contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn's theorem and related results. Larmor's theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the " Eisenhart" or " lightlike" lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdika-Eardley-Nappi-Witten pp-wave solution of Einstein-Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi-Jackiw group. 2011 Elsevier Inc.
