Noncommutative space corrections on the Klein-Gordon and Dirac oscillators spectra. (English) Zbl 1247.81125
Summary: We consider the influence of a noncommutative space on the Klein-Gordon and the Dirac oscillators. The nonrelativistic limit is taken and the \(\theta\)-modified Hamiltonians are determined. The corrections of these Hamiltonians on the energy levels are evaluated in first-order perturbation theory. It is observed a total lifting of the degeneracy to the considered levels. Such effects are similar to the Zeeman splitting in a commutative space.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81R60 | Noncommutative geometry in quantum theory |
References:
| [1] | Seiberg N., J. High Energy Phys. 09 pp 032– |
| [2] | DOI: 10.1103/RevModPhys.73.977 · Zbl 1205.81126 · doi:10.1103/RevModPhys.73.977 |
| [3] | DOI: 10.1016/S0370-1573(03)00059-0 · Zbl 1042.81581 · doi:10.1016/S0370-1573(03)00059-0 |
| [4] | DOI: 10.1007/s10701-009-9349-y · Zbl 1181.83009 · doi:10.1007/s10701-009-9349-y |
| [5] | DOI: 10.1016/S0370-2693(00)00341-5 · Zbl 1050.81568 · doi:10.1016/S0370-2693(00)00341-5 |
| [6] | DOI: 10.1016/S0370-2693(01)00339-2 · Zbl 0977.81046 · doi:10.1016/S0370-2693(01)00339-2 |
| [7] | DOI: 10.1016/S0370-2693(01)01304-1 · Zbl 0977.81048 · doi:10.1016/S0370-2693(01)01304-1 |
| [8] | DOI: 10.1142/S0217732302006977 · Zbl 1083.81542 · doi:10.1142/S0217732302006977 |
| [9] | DOI: 10.1016/j.physletb.2008.11.011 · doi:10.1016/j.physletb.2008.11.011 |
| [10] | DOI: 10.1103/PhysRevD.64.067901 · doi:10.1103/PhysRevD.64.067901 |
| [11] | DOI: 10.1103/PhysRevLett.86.2716 · doi:10.1103/PhysRevLett.86.2716 |
| [12] | DOI: 10.1016/j.physletb.2009.11.003 · doi:10.1016/j.physletb.2009.11.003 |
| [13] | DOI: 10.1088/0305-4470/31/36/002 · Zbl 0951.81507 · doi:10.1088/0305-4470/31/36/002 |
| [14] | DOI: 10.1088/0253-6102/42/5/664 · Zbl 1167.81419 · doi:10.1088/0253-6102/42/5/664 |
| [15] | Riad I. F., J. High Energy Phys. 08 pp 045– |
| [16] | DOI: 10.1017/CBO9780511622755 · doi:10.1017/CBO9780511622755 |
| [17] | Gradshteyn I. S., Table of Integrals, Series and Products (2007) · Zbl 1208.65001 |
| [18] | DOI: 10.1103/PhysRevD.72.025010 · doi:10.1103/PhysRevD.72.025010 |
| [19] | DOI: 10.1088/0305-4470/22/17/002 · doi:10.1088/0305-4470/22/17/002 |
| [20] | DOI: 10.1088/0253-6102/55/3/06 · Zbl 1264.81185 · doi:10.1088/0253-6102/55/3/06 |
| [21] | DOI: 10.1103/PhysRevD.81.085024 · doi:10.1103/PhysRevD.81.085024 |
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