Classification of type A \(N\)-fold supersymmetry. (English) Zbl 1020.81018
Summary: Type A \(N\)-fold supersymmetry of one-dimensional quantum mechanics can be constructed by using \(sl(2)\) generators represented on a finite-dimensional functional space. Using this \(sl(2)\) formalism we show a general method of constructing type A \(N\)-fold supersymmetric models. We also present systematic generation of known models and several new models using this method.
MSC:
| 81Q60 | Supersymmetry and quantum mechanics |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
References:
| [1] | Aoyama, H.; Kikuchi, H.; Okouchi, I.; Sato, M.; Wada, S., Phys. Lett. B, 424, 93 (1998) |
| [2] | Aoyama, H.; Kikuchi, H.; Okouchi, I.; Sato, M.; Wada, S., Nucl. Phys. B, 553, 644 (1999) · Zbl 0958.81013 |
| [3] | Aoyama, H.; Sato, M.; Tanaka, T.; Yamamoto, M., Phys. Lett. B, 498, 117 (2001) · Zbl 0972.81050 |
| [4] | Aoyama, H.; Sato, M.; Tanaka, T., Phys. Lett. B, 503, 423 (2001) · Zbl 0977.81021 |
| [5] | Aoyama, H.; Sato, M.; Tanaka, T. |
| [6] | Aoyama, H.; Nakayama, N.; Sato, M.; Tanaka, T. |
| [7] | Andrianov, A. A.; Ioffe, M. V.; Spiridonov, V. P., Phys. Lett. A, 174, 273 (1993) |
| [8] | Andrianov, A. A.; Ioffe, M. V.; Cannata, F.; Dedonder, J.-P., Int. J. Mod. Phys. A, 10, 2683 (1995) · Zbl 1044.81575 |
| [9] | Andrianov, A. A.; Ioffe, M. V.; Nishnianidze, D. N., Phys. Lett. A, 201, 103 (1995) · Zbl 1020.81597 |
| [10] | Andrianov, A. A.; Ioffe, M. V.; Nishnianidze, D. N., Theor. Math. Phys., 104, 1129 (1995) · Zbl 0855.47044 |
| [11] | Bagrov, V. G.; Samsonov, B. F., Theor. Math. Phys., 104, 1051 (1995) |
| [12] | Samsonov, B. F., Mod. Phys. Lett. A, 11, 1563 (1996) · Zbl 1022.81516 |
| [13] | Bagrov, V. G.; Samsonov, B. F., Phys. Part. Nucl., 28, 374 (1997) |
| [14] | Samsonov, B. F., Phys. Lett. A, 263, 274 (1999) · Zbl 0949.81018 |
| [15] | Plyushchay, M., Int. J. Mod. Phys. A, 15, 3679 (2000) · Zbl 0973.81028 |
| [16] | Klishevich, S.; Plyushchay, M., Mod. Phys. Lett. A, 14, 2739 (1999) |
| [17] | Rosas-Ortiz, J. O., J. Phys. A, 31, 10163 (1998) · Zbl 0934.34074 |
| [18] | Khare, A.; Sukhatme, U., J. Math. Phys., 40, 5473 (1999) · Zbl 0968.81019 |
| [19] | Fernández C. , D. J.; Hussin, V., J. Phys. A, 32, 3630 (1999) |
| [20] | Fernández C. , D. J.; Negro, J.; Nieto, L. M., Phys. Lett. A, 275, 338 (2000) · Zbl 1115.81393 |
| [21] | Witten, E., Nucl. Phys. B, 188, 513 (1981) · Zbl 1258.81046 |
| [22] | Witten, E., Nucl. Phys. B, 202, 253 (1982) |
| [23] | Turbiner, A. V., Commun. Math. Phys., 118, 467 (1988) · Zbl 0683.35063 |
| [24] | Shifman, M. A., Int. J. Mod. Phys. A, 12, 2897 (1989) |
| [25] | Ushveridze, A. G., Quasi-Exactly Solvable Models in Quantum Mechanics (1994), IOP Publishing: IOP Publishing Bristol, and references cited therein · Zbl 0834.58042 |
| [26] | Klishevich, S. M.; Plyushchay, M. S., Nucl. Phys. B, 606, 583 (2001) · Zbl 0969.81543 |
| [27] | Dorey, P.; Dunning, C.; Tateo, R. |
| [28] | Klishevich, S. M.; Plyushchay, M. S. |
| [29] | Aoyama, H.; Kikuchi, H.; Harano, T.; Sato, M.; Wada, S., Phys. Rev. Lett., 79, 4052 (1997) |
| [30] | Aoyama, H.; Kikuchi, H.; Harano, T.; Okouchi, I.; Sato, M.; Wada, S., Prog. Theor. Phys. Suppl., 127, 1 (1997) |
| [31] | H. Aoyama, N. Nakayama, M. Sato, T. Tanaka, in preparation; H. Aoyama, N. Nakayama, M. Sato, T. Tanaka, in preparation |
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.
