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Galilean and Lorentz Transformations in a Space with Generalized Uncertainty Principle

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Abstract

We consider a space with Generalized Uncertainty Principle (GUP) which can be obtained in the frame of the deformed commutation relations. In the space with GUP we have found transformations relating coordinates and times of moving and rest frames of reference in the first order over the parameter of deformation. In the non-relativistic case we find the deformed Galilean transformation which is rotation in Euclidian space–time. This transformation is similar to the Lorentz one but written for Euclidean space–time where the speed of light is replaced by some velocity related to the parameter of deformation. We show that for relativistic particle in the space with GUP the coordinates of the rest and moving frames of reference satisfy the Lorentz transformation with some effective speed of light.

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Acknowledgments

I am grateful to Dr. T. Masłowski for drawing my attention to review [48].

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

    V. M. Tkachuk

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  1. V. M. Tkachuk
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Tkachuk, V.M. Galilean and Lorentz Transformations in a Space with Generalized Uncertainty Principle. Found Phys 46, 1666–1679 (2016). https://doi.org/10.1007/s10701-016-0036-5

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