Kohn’s theorem, Larmor’s equivalence principle and the Newton–Hooke group Academic Article uri icon

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-İnönü 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 Brdička-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.

published proceedings

  • Annals of Physics

author list (cited authors)

  • Gibbons, G. W., & Pope, C. N

citation count

  • 27

complete list of authors

  • Gibbons, GW||Pope, CN

publication date

  • July 2011