Quesne, C.; Tkachuk, V. M. Lorentz-covariant deformed algebra with minimal length. (English) Zbl 1109.81045 Czech. J. Phys. 56, No. 10-11, 1269-1274 (2006). Summary: The \(D\)-dimensional two-parameter deformed algebra with minimal length introduced by Kempf is generalized to a Lorentz-covariant algebra describing a \((D+1)\)-dimensional quantized space-time. For \(D=3\), it includes Snyder algebra as a special case. The deformed Poincaré transformations leaving the algebra invariant are identified. Uncertainty relations are studied. In the case of \(D=1\) and one nonvanishing parameter, the bound-state energy spectrum and wavefunctions of the Dirac oscillator are exactly obtained. Cited in 1 ReviewCited in 13 Documents MSC: 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 17B37 Quantum groups (quantized enveloping algebras) and related deformations Keywords:Dirac equation; supersymmetric quantum mechanics; Poincaré transformations; Uncertainty relations PDF BibTeX XML Cite \textit{C. Quesne} and \textit{V. M. Tkachuk}, Czech. J. Phys. 56, No. 10--11, 1269--1274 (2006; Zbl 1109.81045) Full Text: DOI arXiv OpenURL References: [1] D.J. Gross and P.F. Mende: Nucl. Phys. B303 (1988) 407. [2] D. Amati, M. Ciafaloni and G. Veneziano: Phys. Lett. B216 (1989) 41. [3] H.S. Snyder: Phys. Rev.71 (1947) 38. · Zbl 0035.13101 [4] A. Kempf, G. Mangano and R.B. Mann: Phys. Rev. D52 (1995) 1108. [5] A. Kempf: J. Phys. A30 (1997) 2093. · Zbl 0930.58026 [6] C. Quesne and V.M. Tkachuk: J. Phys. A39 (2006) 10909. · Zbl 1168.81014 [7] D. Itô, K. Mori and E. Carriere: Nuovo Cimento A51 (1967) 1119. [8] M. Moshinsky and A. Szczepaniak: J. Phys. A22 (1989) L817. [9] C. Quesne and V.M. Tkachuk: J. Phys. A38 (2005) 1747. · Zbl 1061.81023 [10] K. Nouicer: J. Phys. A: Math. Gen.39 (2006) 5125. · Zbl 1091.81017 [11] F. Cooper, A. Khare, and U. Sukhatme: Phys. Rep.251 (1995) 267. [12] J. Formánek, R.J. Lombard, and J. Mareš: Czech. J. Phys.54 (2004) 289. [13] J. Kowalski-Glikman and S. Nowak: Int. J. Mod. Phys. D12 (2003) 299. · Zbl 1079.83535 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.