Macroscopic body in the Snyder space and minimal length estimation

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

Received: 24 January 2019
Accepted: 1 March 2019

Abstract

We study the problem of the description of a macroscopic body motion in the frame of the nonrelativistic Snyder model. It is found that the motion of the center-of-mass of a body is described by an effective parameter which depends on the parameters of the Snyder algebra for coordinates and momenta of particles forming the body and their masses. We also show that there is a reduction of the effective parameter with respect to the parameters of the Snyder algebra for coordinates and momenta of individual particles. As a result the problem of the extremely small result for the minimal length obtained on the basis of the studies of the Mercury motion in the Snyder space is solved. In addition we find that the relation of the parameter of the Snyder algebra with the mass opens the possibility to preserve the property of independence of the kinetic energy on composition, to recover the weak equivalence principle, to consider coordinates as kinematic variables, to recover the proportionality of momenta to the mass and to consider the Snyder algebra for the coordinates and momenta of the center-of-mass of a body defined in the traditional way.