[Paper Review] Magnetic Monopoles and Duality Symmetry Breaking in Maxwell's Electrodynamics

Jay R. Yablon|ArXiv.org|Aug 24, 2005

Quantum and Classical Electrodynamics13 references3 citations

TL;DR

This paper proposes a mechanism to break duality symmetry in Maxwell's electrodynamics, preserving electric monopole interactions while suppressing magnetic monopole interactions at low energies. By combining local U(1)EM gauge symmetry with continuous local duality transformations, it derives an emergent SU(2)D duality gauge group, solving the 'zero-charge' problem and explaining the observed dominance of electric over magnetic monopoles.

ABSTRACT

It is shown how to break the symmetry of a Lagrangian with duality symmetry between electric and magnetic monopoles, so that at low energy, electric monopole interactions continue to be observed but magnetic monopole interactions become very highly suppressed to the point of effectively vanishing. The "zero-charge" problem of source-free electrodynamics is solved by requiring invariance under continuous, local, duality transformations, while local duality symmetry combined with local U(1)EM gauge symmetry leads naturally and surprisingly to an SU(2)D duality gauge group.

Motivation & Objective

• To resolve the 'zero-charge' problem in source-free electrodynamics by enforcing invariance under continuous local duality transformations.
• To explain the observed dominance of electric monopoles over magnetic monopoles in nature.
• To derive a consistent gauge structure that unifies local U(1)EM symmetry with duality symmetry.
• To show how duality symmetry breaking naturally leads to the suppression of magnetic monopole interactions at low energies.
• To establish a theoretical framework where magnetic monopoles are effectively absent in the low-energy limit despite their presence in the high-energy Lagrangian.

Proposed method

• Introduce a Lagrangian invariant under continuous local duality transformations, linking electric and magnetic fields.
• Couple local U(1)EM gauge symmetry with local duality symmetry to generate a non-Abelian gauge structure.
• Derive the emergence of an SU(2)D duality gauge group from the combined symmetry algebra.
• Construct a field strength tensor that transforms under both U(1)EM and SU(2)D symmetries.
• Analyze the low-energy limit to show that magnetic monopole interactions are suppressed due to the gauge structure.
• Use the duality anomaly cancellation mechanism to ensure consistency and avoid quantum anomalies.

Experimental results

Research questions

• RQ1 How can duality symmetry in Maxwell's electrodynamics be broken while preserving electric monopole interactions?
• RQ2 What gauge group emerges when local U(1)EM and local duality symmetries are combined?
• RQ3 How does the low-energy limit suppress magnetic monopole interactions despite their presence in the Lagrangian?
• RQ4 Can the 'zero-charge' problem in source-free electrodynamics be resolved through continuous local duality invariance?
• RQ5 What is the role of the SU(2)D duality gauge group in explaining the absence of observable magnetic monopoles?

Key findings

• The combination of local U(1)EM gauge symmetry and continuous local duality symmetry leads to an emergent SU(2)D duality gauge group.
• Magnetic monopole interactions are suppressed at low energies due to the structure of the SU(2)D gauge group, rendering them effectively unobservable.
• The 'zero-charge' problem in source-free electrodynamics is resolved by requiring invariance under continuous local duality transformations.
• The theory remains consistent at the quantum level, with anomalies canceled through the duality anomaly mechanism.
• The model provides a natural explanation for the observed dominance of electric over magnetic monopoles in nature.
• The framework unifies electric and magnetic degrees of freedom at high energies, with spontaneous duality symmetry breaking leading to low-energy electric dominance.