In 1931 Dirac [1] introduced a magnetic monopole into the quantum mechanics and found a quantization relation between an electric charge e and magnetic charge q, 2μ = n, n ∈ Z, where μ = eq, and ~ = c = 1. One of the widely accepted proofs of the Dirac selection rule is based on group representation theory (see, for example, [2, 3, 4, 5, 6]). In the presence of the magnetic monopole the operato...

The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely solved when the magnetic field is produced by a fixed magnetic monopole. The result is applied to central electric field cases, in particular to the time-depen...

We qualitatively discuss the Montonen-Olive electric-magnetic duality in N = 4 supersymmetric Yang-Mills theory with non-maximally broken gauge symmetry, where BPS configurations of massless monopole clouds have been found. We argue that these low energy non-Abelian clouds can be identified as the dual of the infrared bremsstrahlung radiations of the non-Abelian massless particles. After we bre...

Magnetic monopoles and Q-balls are examples of topological nontopological solitons, respectively. A new soliton state with both charges is shown to also exist, given a monopole sector portal coupling an additional scalar field $S$ global $U(1)$ symmetry. This state, the Q-monopole-ball, more stable than isolated Q-ball made only particles, it could be against fissioning into free particles. Sta...

We introduce a gauge invariant topological definition of monopole charge in pure SU(2) gluodynamics. The non-trivial topology is provided by hedgehog configurations of the non-Abelian field strength tensor on the two-sphere surrounding the monopole. It is shown that this definition can be formulated entirely in terms of Wilson loops which makes the gauge invariance manifest. Moreover, it counts...

The SU(2) Yang-Mills-Higgs theory supports the existence of monopoles, antimonopoles, and vortex rings. In this paper, we would like to present new exact static antimonopole-monopole-antimonopole (A-M-A) configurations. The net magnetic charge of these configurations is always negative one, whilst the net magnetic charge at the origin is always positive one for all positive integer values of th...

The SU(2) Yang-Mills-Higgs theory supports the existence of monopoles, antimonopoles, and vortex rings. In this paper, we would like to present new exact static antimonopole-monopole-antimonopole (A-M-A) configurations. The net magnetic charge of these configurations is always negative one, whilst the net magnetic charge at the origin is always positive one for all positive integer values of th...

Magnetic monopole solutions to heterotic string theory are discussed in toroidal compactifications to four spacetime dimensions. Particular emphasis is placed on the relation to previously studied fivebrane solutions in ten dimensions and on the possibility of constructing exact monopole solutions related to symmetric fivebranes.

Dirac's quantization of magnetic monopole strength is derived without reference to a (singular, patched) vector potential.