Electric Charge in Presence of Fixed Monopole-Antimonopole Pair

TL;DR

This paper analyzes the classical and quantum behavior of an electric charge near a fixed monopole-antimonopole pair, revealing potential bound states and implications for confinement mechanisms.

Contribution

It provides a detailed quantum analysis of charge-monopole interactions using variational methods and discusses implications for confinement theories.

Findings

Classical charge can be bound in potential minima or wells.

Quantum states are approximate due to finite potential barriers.

Results suggest possible confinement mechanisms related to dual Meissner effect.

Abstract

The dynamics of an electric charge $e$ in presence of a fixed monopole pair $\pm g$ is considered. Depending on the ratio of the angular momentum to $e\,g/c$, the effective potential may consist a minimum valley between the poles or a finite depth well. In the classical limit the charge may be bound to the poles inside the minimum valley or well. In the quantum theory, due to the finite barrier between the minimum and the potential at infinity, only approximate or quasi bound-states are possible. Based on the Rayleigh-Ritz variational method the energy and eigen-functions are obtained. The implications on the proposed confining mechanism based on the dual picture of the so-called Meissner effect is pointed.