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Foundations of Physics

, Volume 46, Issue 12, pp 1666–1679 | Cite as

Galilean and Lorentz Transformations in a Space with Generalized Uncertainty Principle

  • V. M. Tkachuk
Article

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.

Keywords

Generalized Uncertainty Principle Deformed Heisenberg algebra Minimal length Galilean transformation Lorentz transformation 

Notes

Acknowledgments

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

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department for Theoretical PhysicsIvan Franko National University of LvivLvivUkraine

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