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

Abstract

The (D+1)-dimensional $(\beta ,{\beta }^{\prime })$-two-parameter Lorentz-covariant deformed algebra introduced by Quesne and Tkachuk [C. Quesne and V. M. Tkachuk, J. Phys. A: Math. Gen. \textbf {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 ${\beta }^{\prime }=2\beta$ up to first order over deformation parameter $\beta$. 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 $10^{-17}m<(△X^i{)}_0<10^{-15}m$. Finally, we have shown that the above estimation of minimal length is in good agreement with the results obtained in previous investigations.

10 pages, no figure

References in corpus (7)

• Universality of Quantum Gravity Corrections
• Hydrogen-atom spectrum under a minimal-length hypothesis
• Minimal Length Uncertainty Relation and gravitational quantum well
• Corrections to the ns-levels of hydrogen atom in deformed space with minimal length
• Lorentz-covariant deformed algebra with minimal length
• Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle
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