Lie symmetries for two-dimensional charged particle motion

Abstract

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries.

References in corpus (1)

• Noether symmetries for two-dimensional charged particle motion

Cited by in corpus (6)

• Dynamical symmetries and the Ermakov invariant
• Symmetries of charged particle motion under time-independent electromagnetic fields
• Noether symmetries for charged particle motion under a magnetic monopole and general electric fields
• Group classification of charged particle motion in stationary electromagnetic fields
• Frobenius theorem and invariants for Hamiltonian systems
• Systematic Derivation of Noether Point Symmetries in Special Relativistic Field Theories