Lorentz-covariant deformed algebra with minimal length

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 boundstate energy spectrum and wavefunctions of the Dirac oscillator are exactly obtained. © 2006 Institute of Physics, Academy of Sciences of Czech Republic.SCOPUS: cp.j