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Dirac in 1931 gave a beautiful argument for the quantization of electriccharge, which required only the existence in the universe of one magneticmonopole, because gauge invariance of the interaction between the pole and anycharge could hold only if the product of the charge and the pole strength werequantized in half-integer multiples of the reduced Planck constant. However, ifthe photon had a nonzero mass, implying exponential decrease of the flux out ofan electric charge, then Dirac's argument might seem to fail. We demonstratethat the result still should hold. The key point is that magnetic charge,unlike electric charge, cannot be screened, so that on any surface enclosingthe pole Dirac's string, or equally the Wu-Yang gauge shift, must be present,and to make either of these invisible to charged particles the quantizationcondition is required.

Dirac Quantization Condition Holds with Nonzero Photon Mass