The fine-structure constant, magnetic monopoles and dirac charge quantization condition

Summary

The Dirac quantization condition imposes some very peculiar and stringent constraints on the nature of monopoles. One of the most interesting results is that such a particle has a classical radius larger than its quantum (Compton) or « atomic » (Bohr) radius. No other elementary particle shows this property. This indicates that the monopoles are inherently relativistic. Atom like stable bound states of oppositely charged monopoles are unphysical and a pair of primordial monopoles are prone to annihilation, which may explain the so-called monopole paradox. Conversely, if the value of the Sommerfeld fine-structure constant were greater than unity, then « magnetic-monopole atoms » would have been stable and « electric atoms » unstable. It appears that in a physical universe for a given value of the fine-structure constant only one kind of sources or charges (either electric or magnetic) are permissible. This is a quite general requirement imposed by the laws of electrodynamics, quantum mechanics and relativity acting simultaneously in conjunction to each other.