Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group
arXiv:1010.2455 · doi:10.1016/j.aop.2011.03.003
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.
Typos corrected, references added
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Cited by in corpus (7)
- Hidden Symmetries of Dynamics in Classical and Quantum Physics
- Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
- Schrödinger Symmetry in Gravitational Mini-Superspaces
- Particle motion in circularly polarized vacuum pp waves
- Excited states of exciton-polariton condensates in 2D and 1D harmonic traps
- Equivalence of a harmonic oscillator to a free particle and Eisenhart lift
- Effective field theory for the superfluid vortex lattice from coset construction