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Lorentz-covariant deformed algebra with minimal length

Quantum Physics 2008-11-26 v1 High Energy Physics - Theory Mathematical Physics math.MP

Abstract

The DD-dimensional two-parameter deformed algebra with minimal length introduced by Kempf is generalized to a Lorentz-covariant algebra describing a (D+1D+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.

Keywords

Cite

@article{arxiv.quant-ph/0612093,
  title  = {Lorentz-covariant deformed algebra with minimal length},
  author = {C. Quesne and V. M. Tkachuk},
  journal= {arXiv preprint arXiv:quant-ph/0612093},
  year   = {2008}
}

Comments

8 pages, no figure, presented at XV International Colloquium on Integrable Systems and Quantum Symmetries (ISQS-15), Prague, June 15-17, 2006

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