From the Maxwell's equations point of view, existence of magnetic monopole leads to unsuitability of the introduction of vector potential as $\vec B = \operatorname{rot}\vec A$. As a result, it was introducted by Dirac fiber-like theory of monopole, which is considers a model of monopole as the open end of a semi-infinite solenoid. This is physically unsatisfactory. Another approach, is the introduction of another 4-potential along with $A_{\mu},(\text{where } \mu = 0,1,2,3)$. But such models had problems with formulating in a frame of the principle of least action. And if I'm not mistaken, this problem had been solved (see Magnetic monopoles and Lorentz force). A two-potential models, seems to be more acceptable.
How will the quantization procedure of the electromagnetic field change in two-potential models? Does the photon acquire an additional degree of freedom?
