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Lorentz-covariant deformed algebra with minimal length and application to the (1 + 1)-dimensional Dirac oscillator

par Quesne, Christiane ;Tkachuk, Volodymyr
Référence Journal of Physics A: Mathematical and General, 39, 34, page (10909-10922), 021
Publication Publié, 2006-08

Article révisé par les pairs

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Résumé :

The D-dimensional (β, β′)-two-parameter deformed algebra introduced by Kempf is generalized to a Lorentz-covariant algebra describing a (D + 1)-dimensional quantized spacetime. In the D ≤ 3 and β ≤ 0 case, the latter reproduces Snyder algebra. The deformed Poincaré transformations leaving the algebra invariant are identified. It is shown that there exists a nonzero minimal uncertainty in position (minimal length). The Dirac oscillator in a (1 + 1)-dimensional spacetime described by such an algebra is studied in the case where β′ ≤ 0. Extending supersymmetric quantum mechanical and shape-invariance methods to energy-dependent Hamiltonians provides exact bound-state energies and wavefunctions. Physically acceptable states exist for β < 1/(m2c2). A new interesting outcome is that, in contrast with the conventional Dirac oscillator, the energy spectrum is bounded. © 2006 IOP Publishing Ltd.