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


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.


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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