Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem. (English) Zbl 1370.81169
Summary: In this letter, we study the Aharonov-Bohm problem for a spin-1/2 particle in the quantum deformed framework generated by the \(\kappa\)-Poincaré-Hopf algebra. We consider the nonrelativistic limit of the \(\kappa\)-deformed Dirac equation and use the spin-dependent term to impose an upper bound on the magnitude of the deformation parameter \(\varepsilon\). By using the self-adjoint extension approach, we examine the scattering and bound state scenarios. After obtaining the scattering phase shift and the \(S\)-matrix, the bound states energies are obtained by analyzing the pole structure of the latter. Using our recently developed general regularization prescription [“Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space”, Phys. Rev. D. (3) 85, No. 4, Article ID 041701, 5 p. (2012; doi:10.1103/physrevd.85.041701)], the self-adjoint extension parameter is determined in terms of the physics of the problem. At last, we analyze the problem of helicity conservation.
MSC:
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
Keywords:
\(\kappa\)-Poincaré-Hopf algebra; self-adjoint extension; Aharonov-Bohm; scattering; helicityReferences:
| [1] | Lukierski, J.; Ruegg, H.; Nowicki, A.; Tolstoy, V. N., Phys. Lett. B, 264, 331 (1991) |
| [2] | Lukierski, J.; Nowicki, A.; Ruegg, H., Phys. Lett. B, 293, 344 (1992) · Zbl 0834.17022 |
| [3] | Nowicki, A.; Sorace, E.; Tarlini, M., Phys. Lett. B, 302, 419 (1993) |
| [4] | Biedenharn, L.; Mueller, B.; Tarlini, M., Phys. Lett. B, 318, 613 (1993) |
| [5] | Lukierski, J.; Ruegg, H., Phys. Lett. B, 329, 189 (1994) |
| [6] | Majid, S.; Ruegg, H., Phys. Lett. B, 334, 348 (1994) · Zbl 1112.81328 |
| [7] | Lukierski, J.; Ruegg, H.; Zakrzewski, W., Ann. Phys., 243, 90 (1995) · Zbl 0856.70012 |
| [8] | Agostini, A.; Amelino-Camelia, G.; Arzano, M., Class. Quantum Grav., 21, 2179 (2004) · Zbl 1051.83003 |
| [9] | Aloisio, R.; Galante, A.; Grillo, A. F.; Méndez, F.; Carmona, J. M.; Cortés, J. L., J. High Energy Phys., 0405, 028 (2004) |
| [10] | Kovacević, D.; Meljanac, S.; Pachoł, A.; Strajn, R., Phys. Lett. B, 711, 122 (2012) |
| [11] | Arzano, M.; Marcianò, A., Phys. Rev. D, 76, 125005 (2007) |
| [12] | Roy, P.; Roychoudhury, R., Phys. Lett. B, 339, 87 (1994) |
| [13] | Roy, P.; Roychoudhury, R., Phys. Lett. B, 359, 339 (1995) |
| [14] | Ndimubandi, J., Europhys. Lett., 39, 583 (1997) |
| [15] | Roy, P.; Roychoudhury, R., Mod. Phys. Lett. A, 10, 1969 (1995) |
| [16] | Aharonov, Y.; Bohm, D., Phys. Rev., 115, 485 (1959) · Zbl 0099.43102 |
| [17] | Das, A.; Falomir, H.; Nieto, M.; Gamboa, J.; Méndez, F., Phys. Rev. D, 84, 045002 (2011) |
| [18] | Hohensee, M. A.; Estey, B.; Hamilton, P.; Zeilinger, A.; Müller, H., Phys. Rev. Lett., 108, 230404 (2012) |
| [19] | Correa, F.; Falomir, H.; Jakubsky, V.; Plyushchay, M. S., J. Phys. A, 43, 075202 (2010) · Zbl 1185.81070 |
| [20] | Andrade, F. M.; Silva, E. O.; Pereira, M., Phys. Rev. D, 85, 041701(R) (2012) |
| [21] | Vaidman, L., Phys. Rev. A, 86, 040101 (2012) |
| [22] | Fang, K.; Yu, Z.; Fan, S., Phys. Rev. Lett., 108, 153901 (2012) |
| [23] | Belich, H.; Silva, E. O.; Ferreira, M. M.; Orlando, M. T.D., Phys. Rev. D, 83, 125025 (2011) |
| [24] | Anacleto, M. A.; Brito, F. A.; Passos, E., Phys. Rev. D, 86, 125015 (2012) |
| [25] | Kay, B. S.; Studer, U. M., Commun. Math. Phys., 139, 103 (1991) · Zbl 0727.53087 |
| [26] | Bulla, W.; Gesztesy, F., J. Math. Phys., 26, 2520 (1985) · Zbl 0583.35029 |
| [27] | Albeverio, S.; Gesztesy, F.; Hoegh-Krohn, R.; Holden, H., Solvable Models in Quantum Mechanics (2004), AMS Chelsea Publishing: AMS Chelsea Publishing Providence, RI |
| [28] | de Vega, H. J., Phys. Rev. D, 18, 2932 (1978) |
| [29] | Brandenberger, R. H.; Davis, A.-C.; Matheson, A. M., Nucl. Phys. B, 307, 909 (1988) |
| [30] | Alford, M. G.; Wilczek, F., Phys. Rev. Lett., 62, 1071 (1989) |
| [31] | Harikumar, E.; Sivakumar, M.; Srinivas, N., Mod. Phys. Lett. A, 26, 1103 (2011) · Zbl 1274.81144 |
| [32] | Mohr, P. J.; Taylor, B. N.; Newell, D. B., Rev. Mod. Phys., 84, 1527 (2012) |
| [33] | Gabrielse, G.; Hanneke, D.; Kinoshita, T.; Nio, M.; Odom, B., Phys. Rev. Lett., 97, 030802 (2006) |
| [34] | Gesztesy, F.; Albeverio, S.; Hoegh-Krohn, R.; Holden, H., J. Reine Angew. Math., 1987, 87 (1987) |
| [35] | Dabrowski, L.; Stovicek, P., J. Math. Phys., 39, 47 (1998) · Zbl 0916.47053 |
| [36] | Adami, R.; Teta, A., Lett. Math. Phys., 43, 43 (1998) · Zbl 0907.47058 |
| [37] | Reed, M.; Simon, B., Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-Adjointness (1975), Academic Press: Academic Press New York, London · Zbl 0308.47002 |
| [38] | Sakurai, J. J.; Napolitano, J., Modern Quantum Mechanics (2011), Addison-Wesley |
| [39] | Audretsch, J.; Jasper, U.; Skarzhinsky, V. D., J. Phys. A, 28, 2359 (1995) · Zbl 0864.47046 |
| [40] | Coutinho, F. A.B.; Nogami, Y.; Fernando Perez, J., Phys. Rev. A, 46, 6052 (1992) |
| [41] | de Oliveira, C. R.; Pereira, M., J. Phys. A, 43, 354011 (2010) · Zbl 1196.81226 |
| [42] | (Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions (1972), Dover Publications: Dover Publications New York) · Zbl 0543.33001 |
| [43] | Ruijsenaars, S. N.M., Ann. Phys. (NY), 146, 1 (1983) · Zbl 0554.47003 |
| [44] | Bennaceur, K.; Dobaczewski, J.; Ploszajczak, M., Phys. Rev. C, 60, 034308 (1999) |
| [45] | Goldhaber, A. S., Phys. Rev. D, 16, 1815 (1977) |
| [46] | Sakurai, J. J., Advanced Quantum Mechanics (1967), Addison-Wesley · Zbl 0158.45604 |
| [47] | Bordag, M.; Voropaev, S., Phys. Lett. B, 333, 238 (1994) |
| [48] | Andrade, F. M.; Silva, E. O.; Pereira, M. (2012) |
| [49] | Bordag, M.; Voropaev, S., J. Phys. A, 26, 7637 (1993) |
| [50] | Kazama, Y.; Yang, C. N.; Goldhaber, A. S., Phys. Rev. D, 15, 2287 (1977) |
| [51] | Grossman, B., Phys. Rev. Lett., 50, 464 (1983) |
| [52] | Ganoulis, N., Phys. Lett. B, 298, 63 (1993) |
| [53] | Davis, A.; Martin, A.; Ganoulis, N., Nucl. Phys. B, 419, 323 (1994) |
| [54] | Coutinho, F. A.B.; Perez, J. F., Phys. Rev. D, 49, 2092 (1994) |
| [55] | Araujo, V. S.; Coutinho, F. A.B.; Perez, J. F., J. Phys. A, 34, 8859 (2001) · Zbl 1015.81023 |
| [56] | Bonneau, G.; Faraut, J.; Valent, G., Amer. J. Phys., 69, 322 (2001) |
| [57] | Jackiw, R., Phys. Rev. D, 29, 2375 (1984) |
| [58] | Aharonov, Y.; Casher, A., Phys. Rev. A, 19, 2461 (1979) |
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.
