Applied Mathematics and Physics
ISSN (Print): 2333-4878 ISSN (Online): 2333-4886 Website: http://www.sciepub.com/journal/amp Editor-in-chief: Vishwa Nath Maurya
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Applied Mathematics and Physics. 2014, 2(3), 119-123
DOI: 10.12691/amp-2-3-8
Open AccessResearch Article

On ’t Hooft–Polyakov Monopole, Julia–Zee Dyon, and Higgs Field, throughout the Generalized Bogomoln’yi Equations

Lukasz Andrzej Glinka1,

1B.M. Birla Science Centre, Hyderabad, India

Pub. Date: June 09, 2014
(This article belongs to the Special Issue Towards New Cosmology from Quantum Gravity & Particle Physics)

Cite this paper:
Lukasz Andrzej Glinka. On ’t Hooft–Polyakov Monopole, Julia–Zee Dyon, and Higgs Field, throughout the Generalized Bogomoln’yi Equations. Applied Mathematics and Physics. 2014; 2(3):119-123. doi: 10.12691/amp-2-3-8

Abstract

In this paper, making use of the’tHooft–Polyakov–Julia–Zeeansatz for the SU(2) Yang–Mills–Higgs gauge field theory, we present the straightforward generalization of the Bogomoln’yi equations and its several consequences. Particularly, this is shown that this idea is able to generate new types of non-abelian both dyons and magnetic monopoles and, moreover, that within the new model the scalar field can be described through the Coulomb potential, whereas, upto aconstant, the non-abelian gauge field becomes the Wu–Yang monopole.

Keywords:
gauge field theories SU (2) Yang–Mills–Higgs equations ’t Hooft–Polyakov monopole Julia–Zee dyon Bogomoln’yi equations BPS limit non-abelian dyons non-abelian magnetic monopoles Higgs field Coulomb potential Wu–Yang monopole

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References:

[1]  C.N. Yang, R. Mills. Phys. Rev. 96(1), 191 (1954).
 
[2]  P.W. Higgs. Phys. Rev. Lett. 13, 508 (1964).
 
[3]  J. Schwinger. Phys. Rev. 144, 1087 (1966), 173, 1536 (1968).
 
[4]  Science 165, 757 (1969).
 
[5]  J.J. Aubert et al. Phys. Rev. Lett. 33, 1404 (1974).
 
[6]  J.E. Augustin et al. Phys. Rev. Lett. 33, 1406 (1974).
 
[7]  G. ’t Hooft. Nucl. Phys. B 79, 276 (1974).
 
[8]  A.M. Polyakov. JETP Lett. 20, 194 (1974).
 
[9]  Sov. Phys. JETP 41, 988 (1975).
 
[10]  B. Julia, A. Zee. Phys. Rev. D 11, 2227 (1975).
 
[11]  M.K. Prasad, C.M. Sommerfield. Phys. Rev. Lett. 35, 760 (1975).
 
[12]  E.B. Bogomol’nyi. Sov. J. Nucl. Phys. 24, 449 (1976).
 
[13]  S.-F. Mo, J.-R. Ren, T. Zhu. Commun. Theor. Phys. 51, 293 (2009).
 
[14]  K.M. Milton. Rept. Prog. Phys. 69, 1637 (2006).
 
[15]  M. Creutz. Nucl. Phys. B (Proc. Suppl.) 140, 597 (2005).
 
[16]  G. ’t Hooft. 50 Years of Yang-Mills Theory (World Scientific, 2005).
 
[17]  Ya. Shnir. Magnetic Monopoles (Springer, 2005).
 
[18]  G. Fodor, I. R’ acz. Phys. Rev. Lett. 92, 151801 (2004).
 
[19]  N. Manton, P.M. Sutcli?e. Topological Solitons (Cambridge University Press, 2004).
 
[20]  F.A. Bais, J. Striet. Phys. Lett. B 540, 319 (2002).
 
[21]  X. Artru, D. Fayolle. Prob. Atom. Sci. Tech. 6, 110 (2001).
 
[22]  F.A. Bais, B.J. Schroers. Nucl. Phys. B 512, 250 (1998).
 
[23]  E. van der Meer. Magnetic Monopoles in Gauge Field Theories. On the realization of global symmetries on moduli spaces (MSc thesis, University of Amsterdam, 1997).
 
[24]  D. Singleton. Int. J. Theor. Phys. 34(12), 2453 (1995).
 
[25]  M.A. Shifman. Instantons in Gauge Theories (World Scientific, 1994).
 
[26]  M. Atiyah, N. Hitchin. The Geometry and Dynamics of Magnetic Monopoles (Princeton University Press, 1988).
 
[27]  I.J.R. Aitchinson. Acta Phys. Pol. B 18, 207 (1987).
 
[28]  N.S. Craigie (Ed). Theory and Detection of Magnetic Monopoles in Gauge Theories: A Collected Set of Lecture Notes (World Scientific, 1986).
 
[29]  S. Coleman. Aspects of Symmetry (Cambridge University Press, 1985).
 
[30]  J. Preskill, Ann. Rev. Nucl. Part. Sci. 34, 461 (1984).
 
[31]  R.A. Carrigan, W.P. Trower. Magnetic Monopoles (PlenumPress,1983).
 
[32]  K.L. Chang, W.F. Kao. Chin. J. Phys. 21, 1 (1983).
 
[33]  M.K.Murray, Non-Abelian Magnetic Monopoles (PhDthesis, University of Oxford, 1983).
 
[34]  P. Rossi. Phys. Rep. 86, 317 (1982).
 
[35]  K.L. Chang. Rev. Bras. Fis. 10, 147 (1980).
 
[36]  A. Comtet. Ann. Inst. H. Poincar′e 32, 283 (1980).
 
[37]  D. Wilkinson, F.A. Bais. Phys. Rev. D 19, 2410 (1979).
 
[38]  E. Witten. Phys. Lett. B 86, 283 (1979).
 
[39]  F.A. Bais, H.A. Weldon. Phys. Lett. B 79, 297 (1978).
 
[40]  P. Goddard, D.I. Olive. Rep. Prog. Phys. 41, 1357 (1978).
 
[41]  C. Montonen, D. Olive. Phys. Lett. B 72, 117 (1977).
 
[42]  I. Bialynicki-Birula, Z. Bialynicka-Birula. Phys. Rev. D 3, 2410 (1971).
 
[43]  I. Bialynicki-Birula. Phys. Rev. D 3, 2413 (1971).
 
[44]  D. Zwanziger. Phys. Rev. 176, 1480, 1489 (1968).
 
[45]  T.T. Wu, C.N. Yang. Some Solutions of the Classical Isotopic Gauge Field Equations, in H. Mark, S. Fernbach (Eds). Properties of Matter Under Unusual Conditions (Wiley-Interscience, 1969), pp. 344-354.
 
[46]  L.A.Glinka, AEthereal Multiverse: A New Unifying Theoretical Approach to Cosmology, Particle Physics, and Quantum Gravity (Cambridge In- ternational Science Publishing, 2012).