Charge-monopole trajectories and the WKB approximation

The classical nonrelativistic motion of an electric charge in the presence of a magnetic monopole is reviewed. Using general properties of these trajectories it is shown that the path integral form of the WKB approximation for the charged particle propagator develops an anomalous form for the transition probability density unless the Dirac quantization condition is imposed. This result is shown to be independent of the specific form of the vector potential used to represent the magnetic monopole. The general result is then verified for the specific case that the standard Dirac string solution is used in the path integral. This result is interpreted as an indirect demonstration of the Dirac condition. Other properties of the solutions and the associated action are briefly discussed