We propose a Lorentz-covariant deformed algebra describing a (3 + 1)-dimensional quantized spacetime, which in the nonrelativistic limit leads to undeformed one. The deformed Poincare transformations leaving the algebra invariant are identified. In the classical limit the Lorentz-covariant deformed algebra yields the deformed Lorentz-covariant Poisson brackets. Kepler problem with the deformed Lorentz-covariant Poisson brackets is studied. We obtain that the precession angle of an orbit of the relativistic particle in the gravitational field depends on the mass of the particle, i.e. equivalence principle is violated. We propose a condition for the recovery of the equivalence principle in the space with the deformed Poisson brackets. Comparing our analytical result with the experimental data for the precession angle of Mercury’s orbit we provide an estimation of minimal length.

中文翻译：

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具有变形洛伦兹协变泊松括号的空间开普勒问题

我们提出了一种描述 (3 + 1) 维量化时空的洛伦兹协变变形代数，它在非相对论限制下导致未变形的时空。识别出使代数不变的变形庞加莱变换。在经典极限中，洛伦兹协变变形代数产生变形洛伦兹协变泊松括号。研究了变形洛伦兹协变泊松括号的开普勒问题。我们得到相对论粒子在引力场中轨道的进动角取决于粒子的质量，即违反了等效原理。我们提出了在具有变形泊松括号的空间中恢复等效原理的条件。