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Czechoslovak Journal of Physics

, Volume 56, Issue 10–11, pp 1269–1274 | Cite as

Lorentz-covariant deformed algebra with minimal length

  • C. Quesne
  • V. M. Tkachuk
Article

Abstract

TheD-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. ForD=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 ofD=1 and one nonvanishing parameter, the bound-state energy spectrum and wavefunctions of the Dirac oscillator are exactly obtained.

PACS

03.65.Fd 03.65.Ge 03.65.Pm 11.30.Cp 11.30.Pb 

Key words

deformed algebras Poincaré transformations uncertainty relations Dirac equation supersymmetric quantum mechanics 

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Copyright information

© Springer 2006

Authors and Affiliations

  • C. Quesne
    • 1
  • V. M. Tkachuk
    • 2
  1. 1.Physique Nucléaire Théorique et Physique MathématiqueUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Chair of Theoretical PhysicsIvan Franko Lviv National UniversityLvivUkraine

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