Dynamical symmetry of the magnetic monopole

It is demonstrated that the interaction of a charged particle with a magnetic monopole possesses a large invariance; time can be arbitrarily re-parametrized. When the interaction occurs within conventional, non-relativistic dynamics, the entire theory admits an O(2, 1) conformal group of symmetry transformations, which seems to have escaped notice. Combining this invariance group with the O(3) group of spatial rotations shows that an O(2, 1) × O(3) group of invariances is present, in analogy with the Kepler/Coulomb system. Furthermore, at fixed angular momentum, the dynamics are characterized by a single, irreducible, unitary representation of the conformal O(2, 1) symmetry group, whose Casimir eigenvalue is determined by the monopole strength. Some similar properties of the isotropic harmonic oscillator are also mentioned.