Quantum Theory of a Particle with Electric and Magnetic Charges

Jan Peřina

Iwo Białynicki‐Birula, Zofia Białynicka-Birula

The nonrelativistic quantum theory of a particle having both electric and magnetic charges moving in an arbitrary external electromagnetic field is presented. The theory is based on the hydrodynamic formulation of quantum mechanics. Dirac's quantization condition for the electric and magnetic charges is rederived as a consistency condition for the motion of the probability fluid. Neither the wave function nor the electromagnetic potential, which were the source of ambiguities in all other formulations, appears in our approach. Nevertheless, this theory has all the essential features of the standard quantum mechanics, including the superposition principle.

Jan Peřina

John L. Friedman, Rafael D. Sorkin

The quantum mechanics of a system of nonrelativistic electrically and magnetically charged particles is formulated by introducing as the classical configuration space a certain U(1) bundle over the set of physical particle configurations. In this way one obtains a well-defined and single-valued classical action; and in the corresponding quantum theory, the origin of half-integral spin and of asymptotic Fermi-Dirac statistics in the description of composite systems of bosons finds its expression in terms of the bundle's structure.

Afshin Besharat, Alexander A. Penin

We use the effective field theory approach to systematically study the dynamics of classical and quantum systems in an oscillating magnetic field. We find that the fast field oscillations give rise to an effective interaction which is able to confine charged particles as well as neutral particles with a spin magnetic moment. The effect is reminiscent of the renown dynamical stabilization of charges by the oscillating electric field and provides a foundation for a new class of magnetic traps. The properties characteristic to the dynamical magnetic confinement are reviewed.

John F. Seely