Lorentz-covariant deformed algebra with minimal length
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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.
PACS03.65.Fd 03.65.Ge 03.65.Pm 11.30.Cp 11.30.Pb
Key wordsdeformed algebras Poincaré transformations uncertainty relations Dirac equation supersymmetric quantum mechanics
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