Polymer quantization versus the Snyder noncommutative space

Gorji, Mohammad Ali; Nozari, Kourosh; Vakili, Babak

doi:10.1088/0264-9381/32/15/155007

Cited by 15 publications

(18 citation statements)

References 41 publications

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“…The acceleration (82) contains the singularity due to 푖 ∼ 1/√ 2 − (k k); that is, at V = the acceleration becomes orthogonal to the velocity, but remains divergent. Besides, due to dependence of effective metric on spin, we arrive at rather unusual picture of the Universe with rainbow geometry (some models of doubly special relativity predict rainbow geometry at Planck scale [54][55][56][57]): there is no unique spacetime manifold for the Universe of spinning particles: each particle will probe its own three-dimensional geometry. We conclude that MPTD equations do not seem promising candidate for the description of a relativistic rotating body.…”

Section: Advances In Mathematical Physicsmentioning

confidence: 97%

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Дериглазов

Ramírez

2017

Advances in Mathematical Physics

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We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: (A) one-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic Zitterbewegung; (B) spin-induced noncommutativity and the problem of covariant formalism; (C) three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; (D) paradoxical behavior of the Mathisson-PapapetrouTulczyjew-Dixon equations of a rotating body in ultrarelativistic limit, and equations with improved behavior.

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Section: Advances In Mathematical Physicsmentioning

confidence: 97%

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Дериглазов

Ramírez

2017

Advances in Mathematical Physics

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“…Meanwhile, an alternative scheme for this also exists. One can implement a noncanonical representation of the Heisenberg algebra such that the Hamiltonian operator remains in its standard functional form but the commutation relation is modified as 28,29…”

Section: Introductionmentioning

confidence: 99%

A new bound on polymer quantization via an opto-mechanical setup

Khodadi

Dey

Bhat

et al. 2018

Sci Rep

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The existence of a minimal measurable length as a characteristic length in the Planck scale is one of the main features of quantum gravity and has been widely explored in the context. Various different deformations of spacetime have been employed successfully for the purpose. However, polymer quantization approach is a relatively new and dynamic field towards the quantum gravity phenomenology, which emerges from the symmetric sector of the loop quantum gravity. In this article, we extend the standard ideas of polymer quantization to find a new and tighter bound on the polymer deformation parameter. Our protocol relies on an opto-mechanical experimental setup that was originally proposed to explore some interesting phenomena by embedding the minimal length into the standard canonical commutation relation. We extend this scheme to probe the polymer length deformed canonical commutation relation of the center of mass mode of a mechanical oscillator with a mass around the Planck scale. The method utilizes the novelty of exchanging the relevant mechanical information with a high intensity optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of the current technologies and, thus, it could uncover a decent realization of quantum gravitational phenomena thorough a simple table-top experiment.

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“…For the case of minus sign, clearly there is a maximum value V max = α −1 for the volume of the universe such that V ∈ [0, α −1 ) while V ∈ [0, ∞) for the case of plus sign. At the quantum level, the model with minus sign should be defined on a lattice [25,29] while the model with plus sign leads to the generalized uncertainty relation. Following the way suggested in Ref.…”

Section: Ir-deformed Phase Spacementioning

confidence: 99%

“…From the definition (25) and using the IR-deformed Friedmann equation (15) together with the definition of the effective energy density (18) it is easy to show that…”

Section: Autonomous System and Dynamical Stabilitymentioning

confidence: 99%

Late time cosmic acceleration from natural infrared cutoff

Gorji

2016

Physics Letters B

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In this paper, inspired by the ultraviolet deformation of the Friedmann-Lemaître-Robertson-Walker geometry in loop quantum cosmology, we formulate an infrared-modified cosmological model. We obtain the associated deformed Friedmann and Raychaudhuri equations and we show that the late time cosmic acceleration can be addressed by the infrared corrections. As a particular example, we applied the setup to the case of matter dominated universe. This model has the same number of parameters as ΛCDM, but a dynamical dark energy generates in the matter dominated era at the late time. According to our model, as the universe expands, the energy density of the cold dark matter dilutes and when the Hubble parameter approaches to its minimum, the infrared effects dominate such that the effective equation of state parameter smoothly changes from w eff = 0 to w eff = −2. Interestingly and nontrivially, the unstable de Sitter phase with w eff = −1 is corresponding to Ωm = Ω d = 0.5 and the universe crosses the phantom divide from the quintessence phase with w eff > −1 and Ωm > Ω d to the phantom phase with w eff < −1 and Ωm < Ω d which shows that the model is observationally viable. The results show that the universe finally ends up in a big rip singularity for a finite time proportional to the inverse of the minimum of the Hubble parameter. Moreover, we consider the dynamical stability of the model and we show that the universe starts from the matter dominated era at the past attractor with w eff = 0 and ends up in a future attractor at the big rip with w eff = −2.

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Polymer quantization versus the Snyder noncommutative space

Cited by 15 publications

References 41 publications

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

A new bound on polymer quantization via an opto-mechanical setup

Late time cosmic acceleration from natural infrared cutoff

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