Lorentz-covariant deformed algebra with minimal length
Quantum Physics
2008-11-26 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
The -dimensional two-parameter deformed algebra with minimal length introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ()-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.
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