Kohn’s theorem, Larmor’s equivalence principle and the Newton–Hooke group |
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Authors: | G.W. Gibbons C.N. Pope |
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Affiliation: | aDAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 OWA, UK;bGeorge P. & Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USA |
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Abstract: | 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–?nönü 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 Brdi?ka–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. |
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Keywords: | Group theory Geometry |
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