On Invariant Vectors in the Presence of Electric and Magnetic Fields

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–Sivardièrevector when the system is subject to a magnetic field, and the supergeneralized Runge–Lenz vector for the two-center problem. The application to the 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