Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group
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-Inonu 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 Brdicka-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.
Keywords
Cite
@article{arxiv.1010.2455,
title = {Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group},
author = {G. W. Gibbons and C. N. Pope},
journal= {arXiv preprint arXiv:1010.2455},
year = {2011}
}
Comments
Typos corrected, references added