Magnetic monopoles in gauge field theories

Abstract

An account is given of the new insight into the theory of magnetic monopoles originating from the work of 't Hooft and Polyakov. Their magnetic monopole, associated with the conventional electromagnetic gauge group U( l), 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 twodimensional space-time.Properties of more general monopoles, associated with large gauge groups now thought to be relevant in physics, are discussed. Particular attention is paid to topological properties. Based on this new viewpoint, conjectures can be made about a future quantum theory of monopoles.

Monopoles, vortices, and kinks in the framework of noncommutative geometry

“…The corresponding topological bound is calculated for each case, and verified to be in agreement with standard results. We finally prove, within our unified formalism, that static soliton solutions to the Yang-Mills-Higgs system can only exist when n ≤ 3 [27,28]. This is a generalisation of the well-known result for pure Yang-Mills theory [29], which states that n = 4 is the only dimension in which solitons are allowed.…”

“…As before, that the norm-square of Ω ∓ 4 √ g * (Ω ∧ θ) is non-negative then implies 27) with equality if and only if (4.23) is satisfied. The lower bound for the action is explicitly…”

“…Following the usual case, we may take the action to be I = 1 4e 2 (Ω, Ω), where the dimensionless parameter e plays the rôle of a gauge coupling constant. Under the rescaling ω → eω, it becomes 27) where now…”

Gauge Formulation for Two Potential Theory of Dyons

“…Thus, we see that source free (homogeneous) Maxwell's equations are same as those of equations (1) but the inhomogeneous Maxwell's equations (8) are changed to…”

“…In view of the explanation of CP-violation in terms of non-zero vacuum angle of world [6], the monopoles are necessary dyons and Dirac quantization condition permits dyons to have analogous electric charge. Renewed interests in the subject of monopole has gathered [7,8,9,10] enormous potential importance in connection current grand unified theories, supersymmetric gauge theories and super strings. But unfortunately the experimental searches [11] for these elusive particles have proved fruitless as the monopoles are expected to be super heavy and their typically masses are about two orders of magnitude heavier than the super heavy X bosons mediating proton decay.…”