Classical Mechanics of Many Particles Defined on Canonically Deformed Nonrelativistic Spacetime

Daszkiewicz, Marcin; Walczyk, Cezary J.

doi:10.1142/s0217732311035328

Cited by 22 publications

(36 citation statements)

References 45 publications

(91 reference statements)

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“…So, influence of features of space structures in the Planck scale on composite systems is less than this influence on elementary particles. In addition we have found that commutator for coordinates of the center-of-mass and coordinates of the relative motion is not equal to zero (19) because of noncommutativity (5). So, the motion of the center-of-mass depends on the relative motion in twist-deformed space.…”

Section: Resultsmentioning

confidence: 93%

Features of description of composite system’s motion in twist-deformed spacetime

Gnatenko

2019

Mod. Phys. Lett. A

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Composite system made of N particles is considered in twist-deformed space-time. It is shown that in the space the motion of the center-of-mass of the system depends on the relative motion. Influence of deformation on the motion of the center-of-mass of composite system is less than on the motion of individual particles and depends on the system's composition. We conclude that if we consider commutation relations for coordinates of a particle to be proportional inversely to its mass, the commutation relations for coordinates of composite system do not depend on its composition and are proportional inversely to system's total mass, besides the motion of the center-of-mass is independent of the relative motion. In addition we find that inverse proportionality of parameters of noncommutativity to mass is important for considering coordinates in twist-deformed space as kinematic variables and for preserving of the weak equivalence principle.

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Section: Resultsmentioning

confidence: 93%

Features of description of composite system’s motion in twist-deformed spacetime

Gnatenko

2019

Mod. Phys. Lett. A

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“…It should be also observed that such an extension (blind in A, B indecies) is compatible with canonical deformation (1). Precisely, in τ approaching infinity limit the space (9) with function f (t) = f ±,κ 1 t τ = κ 1 C 2 ± t τ passes into the well-known multiparticle canonical space-time proposed in [45] 4 (see also [46])…”

Section: Twisted N -Enlarged Newton-hooke Space-timesmentioning

confidence: 99%

Quantum Mechanics of Many Particles Defined on Twisted <span class="cmmi-10">N</span>-enlarged Newton–Hooke Space-times

Daszkiewicz¹

2013

Acta Phys. Pol. B

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“…and we can consider the motion of the center-of-mass independently of the relative motion. Taking into account (80) and (13)- (14), equations of motion for the center-of-mass of a body in gravitational field reaḋ…”

Section: Introductionmentioning

confidence: 99%

Parameters of noncommutativity in Lie-algebraic noncommutative space

Gnatenko

2019

Phys. Rev. D

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We find condition on the parameters of noncommutativity on which a list of important results can be obtained in a space with Lie-algebraic noncommutativity. Namely, we show that the weak equivalence principle is recovered in the space, the Poisson brackets for coordinates and momenta of the center-of-mass of a composite system do not depend on its composition and reproduce relations of noncommutative algebra for coordinates and momenta of individual particles if parameters of noncommutativity corresponding to a particle are proportional inversely to its mass. In addition in particular case of Liealgebraic noncommutativity (space coordinates commute to time) on this condition the motion of the center-of-mass is independent of the relative motion and problem of motion of the center-of-mass and problem corresponding to the internal motion can be studied separately.

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Classical Mechanics of Many Particles Defined on Canonically Deformed Nonrelativistic Spacetime

Cited by 22 publications

References 45 publications

Features of description of composite system’s motion in twist-deformed spacetime

Features of description of composite system’s motion in twist-deformed spacetime

Quantum Mechanics of Many Particles Defined on Twisted <span class="cmmi-10">N</span>-enlarged Newton–Hooke Space-times

Parameters of noncommutativity in Lie-algebraic noncommutative space

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