极小长度下实Klein-Gordon场的量子引力修正
Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length
摘要：
Quesne和Tkachuk [C. Quesne和V.M. Tkachuk，J. Phys. A：Math. Gen. \textbf {39}，10909（2006）.]，导致位置的非零最小不确定性（最小长度）。在形变参数$β$上的$β'=2β$达到一阶的情况下，研究了由Quesne-Tkachuk Lorentz协变形变代数描述的（3+1）维时空中的Klein-Gordon方程.结果表明，含有波函数四阶导数的修正Klein-Gordon方程描述了两个质量不同的重粒子。我们已经证明，物理上可接受的质量状态只能存在$β<\frac{1}{8m^{2}c^{2}}$，导致各向同性的最小长度的间隔$10^{-17}m<(\bigtriangleup X^{i})_{0}<10^{-15}m$。最后，我们已经表明，上述估计的最小长度是在很好的协议，在以前的调查中得到的结果。
英文摘要：
The (D+1)-dimensional $(β,β')$-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 $β'=2β$ 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 $β<\frac{1}{8m^{2}c^{2}}$ which leads to an isotropic minimal length in the interval $10^{-17}m<(\bigtriangleup X^{i})_{0}<10^{-15}m$. Finally, we have shown that the above estimation of minimal length is in good agreement with the results obtained in previous investigations.
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