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arXiv · quant-ph/0612093

Lorentz-covariant deformed algebra with minimal length

C. Quesne·V. M. Tkachuk
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Abstract

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.

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C. Quesne, V. M. Tkachuk. 2006-12-12. Lorentz-covariant deformed algebra with minimal length. https://doi.org/10.1007/s10582-006-0436-4

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