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 $\alpha$ 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.

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

References in corpus (2)

• Scaling analysis of the magnetic monopole mass and condensate in the pure U(1) lattice gauge theory
• Phase Transition Couplings in the Higgsed Monopole Model

Cited by in corpus (21)

• Theoretical and Experimental Status of Magnetic Monopoles
• Dual Quantum Electrodynamics: Dyon-Dyon and Charge-Monopole Scattering in a High-Energy Approximation
• Dark Monopoles and SL(2,Z) Duality
• Phase transition in gauge theories, monopoles and the Multiple Point Principle
• Dirac Strings and Monopoles in the Continuum Limit of SU(2) Lattice Gauge Theory
• S-Duality and Helicity Amplitudes
• Anomaly Constraints on Monopoles and Dyons
• Phase Transition in the Higgs Model of Scalar Fields with Electric and Magnetic Charges
• Construction of a Model of Monopolium and its Search via Multi-Photon Channels at LHC
• Monopoles near the Planck Scale and Unification
• Monopoles and Family Replicated Unification
• Family Replicated Gauge Group Models
• Generalized dual symmetry of nonabelian theories and the freezing of α_s
• Duality-symmetric Action for Electromagnetic Theory with Electric and Magnetic Sources
• [SU(3)XSU(2)XU(1)]^2 and Strong Unification
• Phase transition in the Higgs model of scalar dyons
• Scattering Amplitudes for Monopoles: Pairwise Little Group and Pairwise Helicity
• New conformal field theories by gauging electric and magnetic currents
• Phase Transition Couplings in the Higgsed Monopole Model
• Dyons near the Planck scale
• Constraining the Existence of Magnetic Monopoles by Dirac-Dual Electric Charge Renormalization Effect Under the Planck Scale Limit