Short distance versus long distance physics: The classical limit of the minimal length uncertainty relation

Benczik, Sándor; Chang, Lay Nam; Minić, Djordje; Okamura, N.; Rayyan, Saif; Takeuchi, Tatsu

doi:10.1103/physrevd.66.026003

Cited by 234 publications

(257 citation statements)

References 45 publications

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“…The momentum-momentum non-commutativity results to momentum-momentum uncertainty, and in conclusion they lead to one or several minimal momenta, which is a feature of quantization of theories in curved spaces [54,55].…”

Section: Quantization Of the Primary Model And The Gauged Modelmentioning

confidence: 99%

“…As we know, to find Poisson structure between two functions A and B in a phase-space which owns itself a symplectic structure as {ξ α , ξ β } * , one can use the following relation [54,56].…”

Section: Newtonian Dynamics Of a Particle Constrained On An Asymptotimentioning

confidence: 99%

“…So, the free particle's Schrödinger equation includes an added potential which quantizes corresponding energy spectrum. Therefore, by investigating free particle's energy spectrum and comparing with the very spectrum which is obtained via quantum mechanics of the model, one can determine the corresponding parameters [55,56,72].…”

Section: Jhep01(2018)017mentioning

confidence: 99%

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Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

Nejad

Dehghani

Monemzadeh

2018

J. High Energ. Phys.

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Abstract:We study the effect of the simplest geometry which is imposed via the topology of the universe by gauging non-relativistic particle model on torus and 3-torus with the help of symplectic formalism of constrained systems. Also, we obtain generators of gauge transformations for gauged models. Extracting corresponding Poisson structure of existed constraints, we show the effect of the shape of the universe on canonical structure of phase-spaces of models and suggest some phenomenology to prove the topology of the universe and probable non-commutative structure of the space. In addition, we show that the number of extra dimensions in the phase-spaces of gauged embedded models are exactly two. Moreover, in classical form, we talk over modification of Newton's second law in order to study the origin of the terms appeared in the gauged theory.

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Section: Quantization Of the Primary Model And The Gauged Modelmentioning

confidence: 99%

Section: Newtonian Dynamics Of a Particle Constrained On An Asymptotimentioning

confidence: 99%

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Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

Nejad

Dehghani

Monemzadeh

2018

J. High Energ. Phys.

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“…[4][5][6][7][8][9][10][11][12][13]. The idea of modifying the standard Heisenberg uncertainty relation in such a way that it includes a minimal length has first been proposed in the context of quantum gravity and string theory [14,15].…”

Section: Introductionmentioning

confidence: 99%

Hydrogen atom in momentum space with a minimal length

Bouaziz

Ferkous

2010

Phys. Rev. A

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A momentum representation treatment of the hydrogen atom problem with a generalized uncertainty relation,which leads to a minimal length (∆X i ) min = √ 3β + β ′ , is presented. We show that the distance squared operator can be factorized in the case β ′ = 2β. We analytically solve the s-wave bound-state equation. The leading correction to the energy spectrum caused by the minimal length depends on √ β. An upper bound for the minimal length is found to be about 10 −9fm. * Electronic address: djamilbouaziz@mail.univ-jijel.dz

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“…Thus, the picture of spacetime as a continuous differential manifold cannot be valid below Planck length. Furthermore, the existence of a minimum length scale is also a feature of string theory [1]- [5]. In fact, in loop quantum gravity the existence of minimum length turns big bang into a big bounce [6].…”

Section: Introductionmentioning

confidence: 99%

Incorporation of generalized uncertainty principle into Lifshitz field theories

Faizal

Majumder

2015

Annals of Physics

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In this paper, we will incorporation the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bososnic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into an non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.

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Short distance versus long distance physics: The classical limit of the minimal length uncertainty relation

Cited by 234 publications

References 45 publications

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

Hydrogen atom in momentum space with a minimal length

Incorporation of generalized uncertainty principle into Lifshitz field theories

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