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The quantum field theory describing electric and magnetic charges andrevealing a dual symmetry was developed in the Zwanziger formalism. Therenormalization group (RG) equations for both fine structure constants -electric $\alpha$ and magnetic $\tilde \alpha$ - were obtained. It was shownthat the Dirac relation is valid for the renormalized $\alpha $ and $\tilde\alpha$ at the arbitrary scale, but these RG equations can be consideredperturbatively only in the small region: $0.25 \stackrel{<}{\sim} \alpha,\tilde \alpha \stackrel{<}{\sim} 1$ with $\tilde \alpha$ given by the Diracrelation: $\alpha {\tilde \alpha}$ = 1/4.Comment: 15 pages, 4 figures, made corrections of physics after comments from  Kim Milto

DIRAC RELATION AND RENORMALIZATION GROUP EQUATIONS FOR ELECTRIC AND MAGNETIC FINE STRUCTURE CONSTANTS