In Dirac's theory, magnetic monopole is a point-like object which serves as a source of the magnetic field. It is possible to consider a more complicated object which is a source of both the electric field and the magnetic field. Dyons are allowed, but not required by this theory. In quantum theory, the allowed values of the electric and magnetic charges are constrained by the Dirac-Zwanziger-Schwinger quantization condition: if there exists both a particle with electric charge and magnetic charge and a particle with electric charge and magnetic charge , then one must have
where n is an integer, c is the speed of light, and is Planck's constant. This condition follows from the requirement that the wavefunction describing the system of these two particles be univalued (more precisely, it should be a well-defined section of a suitable line bundle on the configuration space of the two particles).
In Grand Unified Theories, dyons can be regarded as excited states of magnetic monopoles. More precisely, the classical magnetic monopole solution has a circle-valued degree of freedom whose semiclassical quantization leads to a tower of states of increasing electric charge. Thus Grand Unified Theories can be said to predict dyons. In particular, it is possible to predict the masses of dyons.