Khai-Ming Wong

Monopole-antimonopole and vortex rings

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 −1, while the net magnetic charge at the origin is always +1 for all positive integer values of the solution’s parameter m. However, when m increases beyond 1, vortex rings appear coexisting with these AMA configurations. The number of vortex rings increases proportionally with the value of m. They are located in space where the Higgs field vanishes along rings. We also show that a single-point singularity in the Higgs field does not necessarily correspond to a structureless 1-monopole at the origin but to a zero-size monopole-antimonopole-monopole (MAM) structure when the solution’s parameter m is odd. This monopole is the Wu-Yang-type monopole and it possesses the Dirac string potential in the Abelian gauge. These exact solutions ...

Monopole–antimonopole pair dyons with critical electric charges

In this paper, we investigate some electrically charged magnetic solutions of the SU(2) Yang–Mills–Higgs field theory in the net-zero topological charge sector. We only examine the case when the Higgs field vanishes at two points along the z-axis and when the Higgs field vanishes along a ring with the z-axis as its symmetry axis. We study the possible electric charges the dyons can carry in relation to the electric–magnetic charge separations and calculate the finite total energy and magnet dipole moment of these dyons. These stationary dyon solutions do not satisfy the first-order Bogomol’nyi equations and are non-BPS solutions. They are axially symmetric saddle-point solutions and are characterized by the electric charge parameter, −1 < η < 1, which determines the net electric charges of these dyons. These dyon solutions are solved numerically when the magnetic charges are n = 1, 2, 3, 4 and 5, and when the strength of the Higgs field potential is non-vanishing with λ = 1. When λ = 1, we found that the net electric charge approaches a finite critical value as η approaches ±1. Hence the electromagnetic charge separation, total energy and magnetic dipole moment of the dyon also approach a finite critical value.

Finite Energy One-half Monopole Solutions of the SU(2) Yang-Mills-Higgs Theory..

We present finite energy SU(2) Yang-Mills-Higgs particles of one-half topological charge. The magnetic fields of these solutions at spatial infinity correspond to the magnetic field of a positive one-half magnetic monopole at the origin and a semi-infinite Dirac string on one-half of the z-axis carrying a magnetic flux of 2π g going into the origin. Hence the net magnetic charge is zero. The gauge potentials are singular along one-half of the z-axis, elsewhere they are regular.

FINITE ENERGY ONE-HALF MONOPOLE SOLUTIONS

We present finite energy SU(2) Yang–Mills–Higgs particles of one-half topological charge. The magnetic fields of these solutions at spatial infinity correspond to the magnetic field of a positive one-half magnetic monopole at the origin and a semi-infinite Dirac string on one-half of the z-axis carrying a magnetic flux of going into the origin. Hence the net magnetic charge is zero. The gauge potentials are singular along one-half of the z-axis, elsewhere they are regular.

JACOBI ELLIPTIC MONOPOLE–ANTIMONOPOLE PAIR SOLUTIONS

We present new classical generalized Jacobi elliptic one monopole–antimonopole pair (MAP) solutions of the SU(2) Yang–Mills–Higgs theory with the Higgs field in the adjoint representation. These generalized 1-MAP solutions are solved with θ-winding number m = 1 and ϕ-winding number n = 1, 2, 3,…,6. Similar to the generalized Jacobi elliptic one monopole solutions, these generalized 1-MAP solutions are solved by generalizing the large distance behavior of the solutions to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing (λ = 0) and nonvanishing (λ = 1). These generalized 1-MAP solutions possess total energies that are comparable to the total energy of the 1-MAP solution with winding number m = 1. However these total energies are significantly lower than the total energy of the 1-MAP solution with winding number m = 2. All these new generalized solutions are regular numerical finite energy non-BPS solutions of the Yang–Mills–Higgs field theory.

The numerical procedures: One-half monopole solutions

We would like to present the numerical procedures of constructing the finite energy SU(2) Yang-Mills-Higgs particles of one-half topological charge. Four types of numerical one-half monopole solutions, Type A1, Type A2, Type B1, and Type B2 solutions have been found from our numerical calculation and comparison are made to investigate whether they are distinct solutions. Our analysis shows that there are two numerically distinct configurations with different total energies, energy density distributions and magnetic dipole moments, namely the Type 1 (A1 and B1) and Type 2 (A2 and B2) respectively. Through our numerical analysis we are able to conclude that the Type A (A1 and A2) and Type B (B1 and B2) solutions are exact 180° rotation of the z-axis about r = 0 of one another. In order to check our numerical accuracy, the calculations are performed by using two different grid sizes, 70 × 60 and 90 × 80, to cover the whole integration regions. We are able to obtain higher accuracy graphs from the latter set ...

Half-monopole in the Weinberg–Salam model

Abstract We present new axially symmetric half-monopole configuration of the SU(2)×U(1) Weinberg–Salam model of electromagnetic and weak interactions. The half-monopole configuration possesses net magnetic charge 2 π / e which is half the magnetic charge of a Cho–Maison monopole. The electromagnetic gauge potential is singular along the negative z -axis. However the total energy is finite and increases only logarithmically with increasing Higgs field self-coupling constant λ 1 / 2 at sin 2 θ W = 0.2312 . In the U(1) magnetic field, the half-monopole is just a one dimensional finite length line magnetic charge extending from the origin r = 0 and lying along the negative z -axis. In the SU(2) ’t Hooft magnetic field, it is a point magnetic charge located at r = 0 . The half-monopole possesses magnetic dipole moment that decreases exponentially fast with increasing Higgs field self-coupling constant λ 1 / 2 at sin 2 θ W = 0.2312 .

Electrically Charged One and a Half Monopole Solution

Recently, we have discussed the coexistence of a finite energy one-half monopole and a ’t Hooft–Polyakov monopole of opposite magnetic charges. In this paper, we would like to introduce electric charge into this new monopoles configuration, thus creating a one-and-a-half dyon. This new dyon possesses finite energy, magnetic dipole moment, and angular momentum and is able to precess in the presence of an external magnetic field. Similar to the other dyon solutions, when the Higgs self-coupling constant,

Monopole-Antimonopole Pair Dyons

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