Asymptotic stability analysis for \(\mathrm{SU}(n)\) dark monopoles. (English) Zbl 1458.81047
Summary: We analyze the asymptotic stability of the \(SU(n)\) Dark Monopole solutions and we show that there are unstable modes associated with them. We obtain the explicit form of the unstable perturbations and the associated negative-squared eigenfrequencies.
MSC:
| 81V60 | Mono-, di- and multipole moments (EM and other), gyromagnetic relations |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
Software:
MathematicaReferences:
| [1] | Corrigan, E.; Olive, D., Color and magnetic monopoles, Nucl. Phys. B, 110, 237 (1976) |
| [2] | Goddard, P.; Olive, D. I., Magnetic monopoles in gauge field theories, Rep. Prog. Phys., 41, 1357 (1978) |
| [3] | Goddard, P.; Olive, D. I., Charge quantization in theories with an adjoint representation Higgs mechanism, Nucl. Phys. B, 191, 511 (1981) |
| [4] | ’t Hooft, G., Magnetic monopoles in unified gauge theories, Nucl. Phys. B, 79, 276 (1974) |
| [5] | Polyakov, A. M., Particle spectrum in the quantum field theory, JETP Lett., 20, 194 (1974) |
| [6] | Deglmann, M. L.Z. P.; Kneipp, M. A.C., Dark monopoles in grand unified theories, J. High Energy Phys., 1901, Article 013 pp. (2019) · Zbl 1409.81144 |
| [7] | Brandt, R. A.; Neri, F., Stability analysis for singular nonabelian magnetic monopoles, Nucl. Phys. B, 161, 253 (1979) |
| [8] | Coleman, S., The magnetic monopole fifty years later, (Zichichi, A., The Unity of the Fundamental Interactions (1983), Springer) |
| [9] | Horváthy, P. A.; O’Raifeartaigh, L.; Rawnsley, J. H., Monopole charge instability, Int. J. Mod. Phys. A, 3, 665 (1988) |
| [10] | Zhang, P. M.; Horvathy, P. A.; Rawnsley, J., Topology, and (in)stability of non-abelian monopoles, Ann. Phys., 327, 118 (2012) · Zbl 1239.81061 |
| [11] | Baacke, J., Fluctuations and stability of the ’t Hooft-Polyakov monopole, Z. Phys. C, 53, 399 (1992) |
| [12] | Shnir, Y. M., Magnetic Monopoles (2005), Springer · Zbl 1084.81001 |
| [13] | Earnshaw, M. A.; James, M., Stability of two doublet electroweak strings, Phys. Rev. D, 48, 5818 (1993) |
| [14] | James, M.; Perivolaropoulos, L.; Vachaspati, T., Detailed stability analysis of electroweak strings, Nucl. Phys. B, 395, 534 (1993) |
| [15] | Hollmann, H., On the stability of gravitating non-abelian monopoles, Phys. Lett. B, 338, 181 (1994) |
| [16] | Bazeia, D.; Santos, M. M., Classical stability of solitons in systems of coupled scalar fields, Phys. Lett. A, 217, 28 (1996) |
| [17] | Achucarro, A.; Urrestilla, J., The (in)stability of global monopoles revisited, Phys. Rev. Lett., 85, 3091 (2000) · Zbl 1369.81063 |
| [18] | Hartmann, B.; Luchini, G.; Constandinidis, C. P.; Pereira, C. F.S., Real scalar field kinks and antikinks and their perturbation spectra in a closed universe, Phys. Rev. D, 101, Article 076004 pp. (2020) |
| [19] | Weinberg, E. J.; Yi, P., Magnetic monopole dynamics, supersymmetry, and duality, Phys. Rep., 438, 65 (2007) |
| [20] | Olsen, H. A.; Oslund, P.; Wu, T. T., On the existence of bound states for a massive spin-one particle and a magnetic monopole, Phys. Rev. D, 42, 665 (1990) |
| [21] | Boulware, D. G.; Brown, L. S.; Cahn, R. N.; Ellis, S. D.; Lee, C., Scattering on magnetic charge, Phys. Rev. D, 14, 2708 (1976) |
| [22] | James, M. E.R., The sphaleron at non-zero Weinberg-angle, Z. Phys. C, 55, 515 (1992) |
| [23] | Weinberg, E. J., Monopole vector spherical harmonics, Phys. Rev. D, 49, 1086 (1994) |
| [24] | Wu, T. T.; Yang, C. N., Dirac monopole without strings: monopole harmonics, Nucl. Phys. B, 107, 365 (1976) |
| [25] | Weinberg, S., Lectures on Quantum Mechanics (2015), Cambridge University Press · Zbl 1335.81005 |
| [26] | Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions (1972), Government Printing Office: Government Printing Office Washington · Zbl 0543.33001 |
| [27] | Dunster, T. M., Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter, SIAM J. Math. Anal., 21, 995 (1990) · Zbl 0703.33002 |
| [28] | Wolfram Research, Inc., Mathematica, version 12.1, Champaign, IL, 2020. |
| [29] | Manton, N. S.; Sutcliffe, P., Topological Solitons (2004), Cambridge University Press · Zbl 1100.37044 |
| [30] | Manton, N. S., The inevitability of sphalerons in field theory, Philos. Trans. R. Soc. A, 377 (2019) |
| [31] | Klinkhamer, F. R.; Manton, N. S., A saddle-point solution in the Weinberg-Salam theory, Phys. Rev. D, 30, 2212 (1984) |
| [32] | Taubes, C. H., The existence of a non-minimal solution to the \(S U(2)\) Yang-Mills-Higgs equations on \(\mathbb{R}^3\): part I, Commun. Math. Phys., 86, 257 (1982) · Zbl 0514.58016 |
| [33] | Taubes, C. H., The existence of a non-minimal solution to the \(S U(2)\) Yang-Mills-Higgs equations on \(\mathbb{R}^3\): part II, Commun. Math. Phys., 86, 299 (1982) · Zbl 0514.58017 |
| [34] | James, M. E.R., Electroweak strings and topology in electroweak theory, Phys. Lett. B, 334, 121 (1994) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
