35 research outputs found

    Comments on the Monopole-Antimonopole Pair Solutions

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    Recently, the monopole-antimonopole pair and monopole-antimonopole chain solutions are solved with internal space coordinate system of θ\theta-winding number mm greater than one. However, we notice that it is also possible to solve these solutions numerically in terms of θ\theta-winding number m=1m=1 instead. When m=1m=1, the exact asymptotic solutions at small and large distances are parameterized by a single integer parameter ss. Here we once again study the monopole-antimonopole pair solution of the SU(2) Yang-Mills-Higgs theory which belongs to the topological trivial sector numerically in its new form. This solution with θ\theta-winding and ϕ\phi-winding number one is parameterized by s=0s=0 at small rr and s=1s=1 at large rr.Comment: Two figures, 13 pages, to be sent for publicatio

    Monopole Solutions of the Massive SU(2) Yang-Mills-Higgs Theory

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    Monopoles in topologically massive gauge theories in 2+1 dimensions with a Chern-Simon mass term have been studied by Pisarski some years ago. He investigated the SU(2) Yang-Mills-Higgs model with an additional Chern-Simon mass term in the action. Pisarski argued that there is a monopole solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by Pisarski. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern-Simon term strength and for several fixed values of Higgs field strength.Comment: 10, pages, 5 figure

    Half-Monopole in the Weinberg-Salam Model

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    We present new axially symmetric half-monopole configuration of the SU(2)×\timesU(1) Weinberg-Salam model of electromagnetic and weak interactions. The half-monopole configuration possesses net magnetic charge 2π/e2\pi/e which is half the magnetic charge of a Cho-Maison monopole. The electromagnetic gauge potential is singular along the negative zz-axis. However the total energy is finite and increases only logarithmically with increasing Higgs field self-coupling constant λ1/2\lambda^{1/2} at sin2θW=0.2312\sin^2\theta_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=0r=0 and lying along the negative zz-axis. In the SU(2) 't Hooft magnetic field, it is a point magnetic charge located at r=0r=0. The half-monopole possesses magnetic dipole moment that decreases exponentially fast with increasing Higgs field self-coupling constant λ1/2\lambda^{1/2} at sin2θW=0.2312\sin^2\theta_W=0.2312.Comment: 14 pages, 3 Figure

    Electrically Charged One and a Half Monopole Solution

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    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, λ\lambda, is nonvanishing, this new dyon solution possesses critical electric charge, total energy, magnetic dipole moment, and dipole separation as the electric charge parameter, η\eta, approaches one. The electric charge and total energy increase with η\eta to maximum critical values as η1\eta\rightarrow1 for all nonvanishing λ\lambda. However, the magnetic dipole moment decreases with η\eta when λ0.1\lambda\geq0.1 and the dipole separation decreases with η\eta when λ1\lambda\geq1 to minimum critical values as η1\eta\rightarrow1.Comment: 24 pages, 7 figures. arXiv admin note: text overlap with arXiv:1208.4893, arXiv:1112.149

    Monopole-Antimonopole Pair Dyons

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    Monopole-antimonopole pair (MAP) with both electric and magnetic charges are presented. The MAP possess opposite magnetic charges but they carry the same electric charges. These stationary MAP dyon solutions possess finite energy but they do not satisfy the first order Bogomol'nyi equations and are not BPS solutions. They are axially symmetric solutions and are characterized by a parameter, 1η1-1\leq\eta\leq 1 which determines the net electric charges of these MAP dyons. These dyon solutions are solved numerically when the magnetic charges of the dipoles are n=±1,±2n=\pm 1, \pm 2 and when the strength of the Higgs field potential λ=0,1\lambda=0, 1. When λ=0\lambda=0, the time component of the gauge field potential is parallel to the Higgs field in isospin space and the MAP separation distance, total energy and net electric charge increase exponentially fast to infinity when η\eta approaches ±1\pm 1. However when λ=1\lambda=1, all these three quantities approach a finite critical value as η\eta approaches ±1\pm 1.Comment: 20 pages, 9 figures, 2 table

    MAP, MAC, and Vortex-rings Configurations in the Weinberg-Salam Model

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    We report on the presence of new axially symmetric monopoles, antimonopoles and vortex-rings solutions of the SU(2)×\timesU(1) Weinberg-Salam model of electromagnetic and weak interactions. When the ϕ\phi-winding number n=1n=1, and 2, the configurations are monopole-antimonopole pair (MAP) and monopole-antimonopole chain (MAC) with poles of alternating sign magnetic charge arranged along the zz-axis. Vortex-rings start to appear from the MAP and MAC configurations when the winding number n=3n=3. The MAP configurations possess zero net magnetic charge whereas the MAC configurations possess net magnetic charge of 4πn/e4\pi n/e. In the MAP configurations, the monopole-antimonopole pair is bounded by the Z0{\cal Z}^0 field flux string and there is an electromagnetic current loop encircling it. The monopole and antimonopole possess magnetic charges ±4πnesin2θW\pm\frac{4\pi n}{e}\sin^2\theta_W respectively. In the MAC configurations there is no string connecting the monopole and the adjacent antimonopole and they possess magnetic charges ±4πne\pm\frac{4\pi n}{e} respectively. The MAC configurations possess infinite total energy and zero magnetic dipole moment whereas the MAP configurations which are actually sphalerons possess finite total energy and magnetic dipole moment. The configurations were investigated for varying values of Higgs self-coupling constant 0λ400\leq \lambda\leq 40 at Weinberg angle θW=π4\theta_W=\frac{\pi}{4}.Comment: 31 pages, 10 figures, 2 table

    Exact Multimonopole Solutions Of The Yang-Mills-Higgs Theory.

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    We found some general exact static multimonopole solutions that satisfy the first order Bogomol'nyi equations and possess infinite energy. These multimonopole solutions can be categorized into two classes, namely the A2 and B2 solutions

    Screening Solutions Of Multimonopole By Unit Charge Antimonopoles.

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    We would like to show in this paper that there exist a whole range of screening solutions of multirnonopole by unit charge antimonopoles in the SU(2) Yang-Mills-Higgs theory
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