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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?

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Particles, which has a fiber-like structure around, like Dirac's monopole, I meant physical usatisfactory. –  Sergio Mar 9 '12 at 12:49
A two potential models, I seem to be more acceptable. –  Sergio Mar 9 '12 at 12:56
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