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On the nature of fermion-monopole supersymmetry.(English)Zbl 1050.81690

Summary: It is shown that the generator of the nonstandard fermion-monopole supersymmetry uncovered by De Jonghe, Macfarlane, Peeters and van Holten, and the generator of its standard \(N=1/2\) supersymmetry have to be supplemented by their product operator to be treated as independent supercharge. As a result, the fermion-monopole system possesses the nonlinear \(N=3/2\) supersymmetry having the nature of the 3D spin-1/2 free particle’s supersymmetry generated by the supercharges represented in a scalar form. Analyzing the supercharges’ structure, we trace how under reduction of the fermion-monopole system to the spherical geometry the nonlinear \(N=3/2\) superalgebra comprising the Hamiltonian and the total angular momentum as even generators is transformed into the standard linear \(N=1\) superalgebra with the Hamiltonian to be the unique even generator.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations

Cite

References:

[1]De Jonghe, F.; Macfarlane, A. J.; Peeters, K.; van Holten, J. W., Phys. Lett. B, 359, 114 (1995), hep-th/9507046
[2]E. d’Hoker, L. Vinet, Phys. Lett. 137 B (1984) 72.; E. d’Hoker, L. Vinet, Phys. Lett. 137 B (1984) 72.
[3]Gibbons, G. W.; Rietdijk, R. H.; van Holten, J. W., Nucl. Phys. B, 404, 42 (1993), hep-th/9303112 ·Zbl 1043.83545
[4]van Holten, J. W., Phys. Lett. B, 342, 47 (1995), hep-th/9409139
[5]Tanimoto, M., Nucl. Phys. B, 442, 549 (1995), gr-qc/9501006
[6]Grignani, G.; Plyushchay, M.; Sodano, P., Nucl. Phys. B, 464, 189 (1996), hep-th/9511072 ·Zbl 1004.81552
[7]Nirov, Kh. S.; Plyushchay, M. S., Nucl. Phys. B, 512, 295 (1998), hep-th/9803221 ·Zbl 0947.81037
[8]M.S. Plyushchay, Monopole Chern-Simons term: charge-monopole system as a particle with spin, hep-th/0004032.; M.S. Plyushchay, Monopole Chern-Simons term: charge-monopole system as a particle with spin, hep-th/0004032. ·Zbl 1060.81554
[9]Cooper, F.; Khare, A.; Sukhatme, U., Phys. Rep., 251, 267 (1995), hep-th/9405029
[10]Jackiw, R., Ann. Phys. (NY), 129, 183 (1980)
[11]Gamboa, J.; Plyushchay, M., Nucl. Phys. B, 512, 485 (1998), hep-th/9711170 ·Zbl 0947.81555
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.
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