Classical symmetries of monopole by group theoretic methods

TL;DR

This paper employs group theoretic techniques to identify and analyze the symmetries of equations describing a charged particle in monopole fields and near black hole horizons, revealing their Lie algebra structures.

Contribution

It provides a systematic derivation of the extended Lie point symmetries and complete symmetry groups for monopole equations and related physical models.

Findings

Derived generators and Lie algebras for monopole symmetry groups

Identified symmetries of particle equations near black hole horizons

Analyzed specific magnetic field and potential cases

Abstract

We use group theoretic methods to obtain the extended Lie point symmetries of the equations of motion for a charged particle in the field of a monopole. Cases with certain model magnetic fields and potentials are also studied. Our analysis gives the generators and Lie algebras generating the inherent symmetries. The equations of motion of a scalar particle probing the near horizon structure of a black hole is also treated likewise. We have also found the generators of Krause's complete symmetry groups for some of the above examples.