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

TL;DR

This paper develops renormalization group equations for electric and magnetic fine structure constants within the Zwanziger formalism, demonstrating the validity of the Dirac relation at arbitrary scales and its perturbative applicability in a specific coupling range.

Contribution

It derives RG equations for electric and magnetic fine structure constants in a dual symmetric quantum field theory, extending understanding of their scale dependence and the Dirac relation.

Findings

RG equations valid at arbitrary scales for renormalized constants

Dirac relation holds for renormalized couplings at any scale

Perturbative regime limited to small coupling values between 0.25 and 1

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 $\alpha$ and magnetic $\tilde \alpha$ - were obtained. It was shown that the Dirac relation is valid for the renormalized $\alpha $ and $\tilde \alpha$ at the arbitrary scale, but these RG equations can be considered perturbatively only in the small region: $0.25 \stackrel{<}{\sim} \alpha, \tilde \alpha \stackrel{<}{\sim} 1$ with $\tilde \alpha$ given by the Dirac relation: $\alpha {\tilde \alpha}$ = 1/4.