dorsal/arxiv
View SchemaLorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator
| Authors | C. Quesne, V. M. Tkachuk |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604118 |
| URL | https://arxiv.org/abs/quant-ph/0604118 |
| DOI | 10.1088/0305-4470/39/34/021 |
| Journal | J.Phys.A39:10909-10922,2006 |
Abstract
The $D$-dimensional $(\beta, \beta')$-two-parameter deformed algebra introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. In the D=3 and $\beta=0$ case, the latter reproduces Snyder algebra. The deformed Poincar\'e 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 space-time described by such an algebra is studied in the case where $\beta'=0$. Extending supersymmetric quantum mechanical and shape-invariance methods to energy-dependent Hamiltonians provides exact bound-state energies and wavefunctions. Physically acceptable states exist for $\beta < 1/(m^2 c^2)$. A new interesting outcome is that, in contrast with the conventional Dirac oscillator, the energy spectrum is bounded.
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"abstract": "The $D$-dimensional $(\\beta, \\beta\u0027)$-two-parameter deformed algebra\nintroduced by Kempf is generalized to a Lorentz-covariant algebra describing a\n($D+1$)-dimensional quantized space-time. In the D=3 and $\\beta=0$ case, the\nlatter reproduces Snyder algebra. The deformed Poincar\\\u0027e transformations\nleaving the algebra invariant are identified. It is shown that there exists a\nnonzero minimal uncertainty in position (minimal length). The Dirac oscillator\nin a 1+1-dimensional space-time described by such an algebra is studied in the\ncase where $\\beta\u0027=0$. Extending supersymmetric quantum mechanical and\nshape-invariance methods to energy-dependent Hamiltonians provides exact\nbound-state energies and wavefunctions. Physically acceptable states exist for\n$\\beta \u003c 1/(m^2 c^2)$. A new interesting outcome is that, in contrast with the\nconventional Dirac oscillator, the energy spectrum is bounded.",
"arxiv_id": "quant-ph/0604118",
"authors": [
"C. Quesne",
"V. M. Tkachuk"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP",
"math.QA"
],
"doi": "10.1088/0305-4470/39/34/021",
"journal_ref": "J.Phys.A39:10909-10922,2006",
"title": "Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator",
"url": "https://arxiv.org/abs/quant-ph/0604118"
},
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