Noncommutative geometry of the quantum clock

Mignemi, Salvatore; Uras, Nicola

doi:10.1016/j.physleta.2019.01.002

Cited by 5 publications

(7 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This occurs for example in a recently proposed model based on the quantum clock. 40 In this case our proof is not valid and the two definitions of velocity might give rise to different predictions. In fact, the argument of the previous section relies on the fact that under the given hypotheses the trajectories are straight lines and the velocity is constant.…”

Section: Generalization To Coordinate-dependent Poisson Bracketsmentioning

confidence: 86%

Physical velocity of particles in relativistic curved momentum space

Mignemi

Rosati

2020

Mod. Phys. Lett. A

View full text Add to dashboard Cite

We show in general that for a relativistic theory with curved momentum space, i.e. a theory with deformed relativistic symmetries, the physical velocity of particles coincides with their group velocity. This clarifies a long-standing question about the discrepancy between coordinate and group velocity for this kind of theories. The first evidence that this was the case had been obtained at linear order in the deformation parameter in Ref. 1 for the specific case of [Formula: see text]-momentum space. The proof was based on the recent understanding of how relative locality affects these scenarios. Here we rely again on a careful implementation of relative locality effects, and obtain our result for a generic (relativistic) curved momentum space framework at all orders in the deformation/curvature parameter. We also discuss the validity of this result when the deformation depends on the coordinates as well as on the momenta.

show abstract

Section: Generalization To Coordinate-dependent Poisson Bracketsmentioning

confidence: 86%

Physical velocity of particles in relativistic curved momentum space

Mignemi

Rosati

2020

Mod. Phys. Lett. A

View full text Add to dashboard Cite

show abstract

“…We study the relativistic motion of a charged particle in a static magnetic field. Since the Poincaré algebra is undeformed in the quantum clock geometry [3], we take as Hamiltonian the standard relativistic one,…”

Section: The Modelmentioning

confidence: 99%

“…Here, we describe a new effect, related to the motion of a particle in a constant magnetic field. We shall consider a recently proposed model of noncommutative geometry [3], inspired by the discussion of a quantum clock [4], since in that case the calculations are particularly simple. A quantum clock is a device that measures time through the decay of a sample of radioactive matter.…”

Section: Introductionmentioning

confidence: 99%

“…Its nature entails an uncertainty relation between the interval of time measured and the size of the clock [4]. This uncertainty relation can be derived in a relativistic quantum mechanical setting by postulating a deformation of the Heisenberg algebra, in which the time and space coordinates have nontrivial commutation relations [3].…”

Section: Introductionmentioning

confidence: 99%

“…A possibility of observing the deformation may however come from periodic motion. In [3] were for example considered planetary orbits in a Schwarzschild background and corrections to the period of orbits predicted by general relativity were found. However, it is unlikely that noncommutative geometries are effective in such macroscopic situations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Cyclotron frequency and the quantum clock

Mignemi

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

κ -deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra, and dispersion relations

Meljanac

Mignemi

et al. 2019

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

We consider κ-deformed relativistic quantum phase space and possible implementations of the Lorentz algebra. There are two ways of performing such implementations. One is a simple extension where the Poincaré algebra is unaltered, while the other is a general extension where the Poincaré algebra is deformed. As an example we fix the Jordanian twist and the corresponding realization of noncommutative coordinates, coproduct of momenta and addition of momenta. An extension with a one-parameter family of realizations of the Lorentz generators, dilatation and momenta closing the Poincaré-Weyl algebra is considered. The corresponding physical interpretation depends on the way the Lorentz algebra is implemented in phase space. We show how the spectrum of the relativistic hydrogen atom depends on the realization of the generators of the Poincaré-Weyl algebra. * Daniel.Meljanac@irb.hr † meljanac@irb.hr ‡ smignemi@unica.it § rina.strajn@unidu.hr

show abstract

Noncommutative geometry of the quantum clock

Cited by 5 publications

References 22 publications

Physical velocity of particles in relativistic curved momentum space

Physical velocity of particles in relativistic curved momentum space

Cyclotron frequency and the quantum clock

κ -deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra, and dispersion relations

Contact Info

Product

Resources

About