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International Journal of Theoretical Physics

, Volume 49, Issue 9, pp 2080–2088 | Cite as

Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length

  • S. K. Moayedi
  • M. R. SetareEmail author
  • H. Moayeri
Article

Abstract

The (D+1)-dimensional (β,β′)-two-parameter Lorentz-covariant deformed algebra introduced by Quesne and Tkachuk (J. Phys., A Math. Gen. 39, 10909, 2006), leads to a nonzero minimal uncertainty in position (minimal length). The Klein-Gordon equation in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where β′=2β up to first order over deformation parameter β. It is shown that the modified Klein-Gordon equation which contains fourth-order derivative of the wave function describes two massive particles with different masses. We have shown that physically acceptable mass states can only exist for \(\beta<\frac{1}{8m^{2}c^{2}}\) which leads to an isotropic minimal length in the interval 10−17 m<(ΔX i )0<10−15 m. Finally, we have shown that the above estimation of minimal length is in good agreement with the results obtained in previous investigations.

Keywords

Quantum gravity Minimal length Relativistic wave equations Klein-Gordon equation 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of PhysicsArak UniversityArakIran
  2. 2.Department of SciencePayame Noor UniversityBijarIran

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