Lorentz-covariant deformed algebra with minimal length

Details Lorentz-covariant deformed algebra with minimal length Lorentz-covariant deformed algebra with minimal length

2006-12-12

arxiv.org/abs/quant-ph/0612093v1

Czech.J.Phys.56:1269-1274,2006

Physics

Quantum Physics

8 pages, no figure, presented at XV International Colloquium on Integrable Systems and Quantum Symmetries (ISQS-15), Prague, J

Scientific paper

10.1007/s10582-006-0436-4

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 Poincar\'e 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.

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