Preprint Review Version 1 Preserved in Portico This version is not peer-reviewed

On Invariant Vectors in the Presence of Electric and Magnetic Fields

Version 1 : Received: 6 June 2023 / Approved: 7 June 2023 / Online: 7 June 2023 (08:19:04 CEST)

A peer-reviewed article of this Preprint also exists.

Pain, J.-C. On Invariant Vectors in the Presence of Electric and Magnetic Fields. Atoms 2023, 11, 105. Pain, J.-C. On Invariant Vectors in the Presence of Electric and Magnetic Fields. Atoms 2023, 11, 105.

Abstract

In this non-exhaustive review, we discuss the importance of invariant vectors in atomic physics, such as the Laplace-Runge-Lenz vector, the Redmond vector in the presence of an electric field, the Landau-Avron-Sivardière vector when the system is subject to a magnetic field, and the supergeneralized Runge-Lenz vector for the two-center problem. Application to Stark and Zeeman effects are outlined. The existence of constants of motion in the charge-dyon system is also briefly mentioned.

Keywords

symmetry; invariant vectors; Hermann-Bernoulli-Laplace-Runge-Lenz vector; Redmond invariant; dynamical symmetry; supergeneralized Runge-Lenz vector; Kustaanheimo-Stiefel transformation; charge-dyon system; MIC-Kepler problem

Subject

Physical Sciences, Atomic and Molecular Physics

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