Mass Spectrum and Correlation Functions of Nonabelian Quantum Magnetic Monopoles

TL;DR

This paper applies a duality-based quantization method to analyze quantum monopoles in the SO(3) Georgi-Glashow model, deriving their mass, charge, and correlation functions, and confirming consistency with classical bounds.

Contribution

It introduces a novel quantization approach for nonabelian monopoles and explicitly computes their quantum properties within the Georgi-Glashow model.

Findings

Quantum monopoles carry 4π/g units of magnetic charge.

The asymptotic monopole correlation function is explicitly derived.

The quantum monopole mass satisfies the Bogomolnyi bound.

Abstract

The method of quantization of magnetic monopoles based on the order-disorder duality existing between the monopole operator and the lagrangian fields is applied to the description of the quantum magnetic monopoles of `t Hooft and Polyakov in the SO(3) Georgi-Glashow model. The commutator of the monopole operator with the magnetic charge is computed explicitly, indicating that indeed the quantum monopole carries $4\pi/g$ units of magnetic charge. An explicit expression for the asymptotic behavior of the monopole correlation function is derived. From this, the mass of the quantum monopole is obtained. The tree-level result for the quantum monopole mass is shown to satisfy the Bogomolnyi bound ($M_{\rm mon} \geq 4 \pi \frac{M}{g^2}$) and to be within the range of values found for the energy of the classical monopole solution.