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ISOSPIN PARTICLE ON S² WITH ARBITRARY NUMBER OF SUPERSYMMETRIES

SOON-TAE HONG

Department of Science Education and Research Institute for Basic Sciences, Ewha Womans University, Seoul 120-750, Korea

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JOOHAN LEE

Department of Physics, University of Seoul, Seoul 130-743, Korea

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TAE HOON LEE

Department of Physics and Institute of Natural Sciences, Soongsil University, Seoul 156-743, Korea

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, and

PHILLIAL OH

Department of Physics and Institute of Basic Science, Sungkyunkwan University, Suwon 440-746, Korea

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https://doi.org/10.1142/S0217732307023857Cited by:4 (Source: Crossref)

Abstract

We study the supersymmetric quantum mechanics of an isospin particle in the background of spherically symmetric Yang–Mills gauge field. We show that on S² the number of supersymmetries can be made arbitrarily large for a specific choice of the spherically symmetric SU(2) gauge field. However, the symmetry algebra containing the supercharges becomes nonlinear if the number of fermions is greater than two. We present the exact energy spectra and eigenfunctions, which can be written as the product of monopole harmonics and a certain isospin state. We also find that the supersymmetry is spontaneously broken if the number of supersymmetries is even.

Keywords:

PACS: 11.30.Pb, 11.30.Qc, 12.60.Jv, 14.80.Hv

References

S. R. Coleman, The Magnetic Monopole Fifty Years Later, in Les Houches Summer School (1981) 461 . Google Scholar
P. Goddard and D. I. Olive, Rep. Prog. Phys. 41, 1357 (1978), DOI: 10.1088/0034-4885/41/9/001. Crossref, Web of Science, ADS, Google Scholar
R. Jackiw, Ann. Phys. 129, 183 (1980). Crossref, Web of Science, ADS, Google Scholar
E. D'Hoker and L. Vinet, Phys. Lett. B 137, 72 (1984). Crossref, Web of Science, ADS, Google Scholar
D. Spector, Phys. Lett. B 474, 331 (2000). Crossref, Web of Science, ADS, Google Scholar
M. S. Plyushchay, Phys. Lett. B 485, 187 (2000). Crossref, Web of Science, ADS, Google Scholar
C. Leiva and M. S. Plyushchay, Phys. Lett. B 582, 135 (2004). Crossref, Web of Science, ADS, Google Scholar
S. Kim and C. Lee, Ann. Phys. 296, 390 (2002). Crossref, Web of Science, ADS, Google Scholar
F. De Jongheet al., Phys. Lett. B 359, 114 (1995). Crossref, Web of Science, ADS, Google Scholar
N. Linden, A. J. Macfarlane and J. W. van Holten, Phys. Lett. B 373, 125 (1996). Web of Science, Google Scholar
S. T. Honget al., JHEP 0602, 036 (2006). ADS, Google Scholar
S. T. Honget al., Phys. Rev. D 72, 015002 (2005), DOI: 10.1103/PhysRevD.72.015002. Crossref, Web of Science, Google Scholar
S. T. Honget al., Phys. Lett. B 628, 165 (2005). Crossref, Web of Science, ADS, Google Scholar
T. T. Wu and C. N. Yang, Properties of Matter Under Unusual Conditions, eds. H. Mark and S. Fernbach (Interscience, 1969) pp. 349–354. Google Scholar
T. T. Wu and C. N. Yang, Phys. Rev. D 12, 3843 (1975), DOI: 10.1103/PhysRevD.12.3843. Crossref, Web of Science, ADS, Google Scholar
A. Pais and V. Rittenberg, J. Math. Phys. 16, 2062 (1975), DOI: 10.1063/1.522421. Crossref, Web of Science, Google Scholar
P. G. O. Freund and I. Kaplansky, J. Math. Phys. 17, 228 (1976), DOI: 10.1063/1.522885. Crossref, Web of Science, ADS, Google Scholar
M. Scheunert, W. Nahm and V. Rittenberg, J. Math. Phys. 18, 155 (1977), DOI: 10.1063/1.523149. Crossref, Web of Science, ADS, Google Scholar
M. Marcu, J. Math. Phys. 21, 1277 (1980), DOI: 10.1063/1.524576. Crossref, Web of Science, ADS, Google Scholar
A. P. Balachandranet al., Phys. Rev. D 15, 2308 (1977), DOI: 10.1103/PhysRevD.15.2308. Crossref, Web of Science, ADS, Google Scholar
S. K. Wong, Nuovo Cimento A 65, 689 (1972), DOI: 10.1007/BF02892134. Crossref, ADS, Google Scholar
T. T. Wu and C. N. Yang, Nucl. Phys. B 107, 365 (1976), DOI: 10.1016/0550-3213(76)90143-7. Crossref, Web of Science, ADS, Google Scholar