Magnetic monopoles in gauge field theories

TLDR

Magnetic monopoles arise as finite‑energy smooth soliton solutions in SU(2) gauge theory, a concept developed by ’t Hooft and Polyakov. Properties of more general monopoles associated with large gauge groups are discussed, and conjectures about a future quantum theory of monopoles are proposed. A precise picture of the monopole’s internal structure, magnetic charge, and mass is obtained, linking the Dirac monopole and the Sine‑Gordon soliton.

Abstract

An account is given of the new insight into the theory of magnetic monopoles originating from the work of 't Hooft (1976) and Polyakov (1974). Their magnetic monopole, associated with the conventional electromagnetic gauge group U(1), occurs as a finite-energy smooth soliton solution to an SU(2) gauge theory. A precise picture of its internal structure, the values of its magnetic charge and its mass are obtained. These new developments bring together previously unrelated fields of study, namely the Dirac monopole (with point structure) and the Sine-Gordon soliton in two-dimensional space-time. Properties of more general monopoles, associated with large gauge groups now thought to be relevant in physics, are discussed. Based on this new viewpoint, conjectures can be made about a future quantum theory of monopoles.