Geometrical Aspects of Motion of Charged Particles in Magnetic and Killing Magnetic Fields and Their Corresponding Trajectories in Anti-De Sitter 3-Space

Abstract

We inquire the motion of charged particles varying under the effect of Lorentz force produced by magnetic and Killing magnetic fields in anti-de Sitter 3-space . Primarily, we characterize magnetic trajectories in in terms of their Frenet apparatus. Thereafter, utilizing a geometrical model of split-quaternions for (where corresponds to a subspace of the Lie group H of split-quaternions) we find 6 independent unit Killing vector fields on which constitutes a basis for the corresponding 6D Lie algebra i(). We conclude with characterizations of Killing magnetic trajectories in with respect to quasi-slope, curvature and torsion or pseudo-torsion (depending on the situation).

AMS Classification:

• 53C22
• 53C40
• 53C50
• 53Z05
• 78A35

Keywords:

• Anti-de Sitter 3-space
• Frenet apparatus
• Magnetic field
• Lorentz force
• Magnetic trajectory
• Split-quaternion
• Killing vector field