## Lorentz-covariant deformed algebra with minimal length.(English)Zbl 1109.81045

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.

### MSC:

 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 17B37 Quantum groups (quantized enveloping algebras) and related deformations
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### References:

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