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Kepler Problem in Space with Deformed Lorentz-Covariant Poisson Brackets

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Abstract

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 Poincaré 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.

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Acknowledgements

This work was supported in part by the European Commission under the project STREVCOMS PIRSES-2013-612669 and by the projects FF-63Hp (Grant No. 0117U007190) and FF-30F (Grant No. 0116U001539) from the Ministry of Education and Science of Ukraine. The authors thank Dr. A. A. Rovenchak for a careful reading of the manuscript.

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  1. Department for Theoretical Physics, Ivan Franko National University of Lviv, 12 Drahomanov St., Lviv, UA, 79005, Ukraine

    M. I. Samar & V. M. Tkachuk

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Samar, M.I., Tkachuk, V.M. Kepler Problem in Space with Deformed Lorentz-Covariant Poisson Brackets. Found Phys 50, 942–959 (2020). https://doi.org/10.1007/s10701-020-00359-z

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