Dirac Relation and Renormalization Group Equations for Electric and Magnetic Fine Structure Constants

Abstract

The quantum field theory describing electric and magnetic charges and revealing a dual symmetry was developed in the Zwanziger formalism. The renormalization group (RG) equations for both fine structure constants - electric $α$ and magnetic $\tilde α$ - were obtained. It was shown that the Dirac relation is valid for the renormalized $α$ and $\tilde α$ at the arbitrary scale, but these RG equations can be considered perturbatively only in the small region: $0.25 \stackrel{<}{\sim} α, \tilde α\stackrel{<}{\sim} 1$ with $\tilde α$ given by the Dirac relation: $α{\tilde α}$ = 1/4.

15 pages, 4 figures, made corrections of physics after comments from Kim Milton