Generalized uncertainty principle, modified dispersion relations and the early universe thermodynamics

Nozari, Kourosh; Fazlpour, Behnaz

doi:10.1007/s10714-006-0331-0

Cited by 76 publications

(61 citation statements)

References 30 publications

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“…[248, 318, 437, 273]) establish a connection with previous attempts at replacing inflation by scenarios accommodating departures from Lorentz symmetry, such as the scenario with a time-varying speed of light, introduced in works by Moffat [419] and in works by Albrecht and Magueijo [30] (see also Ref. [104]).…”

Section: Quantum-spacetime Cosmologymentioning

confidence: 79%

Quantum-Spacetime Phenomenology

Amelino‐Camelia

2013

Living Rev. Relativ.

748

874

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Section: Quantum-spacetime Cosmologymentioning

confidence: 79%

Quantum-Spacetime Phenomenology

Amelino‐Camelia

2013

Living Rev. Relativ.

748

874

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“…Theories such as E-infinity and scale relativity which are based on fractal structure of spacetime at very short distances may provide a suitable framework for formulation of this short distance thermodynamics. The signature of this non-standard thermodynamics has been seen in other problems such as very early universe [36]. Currently there is no explicit formulation of such a short distance formalism but in any case it should be based on fractal nature of spacetime at quantum gravity level.…”

Section: Discussionmentioning

confidence: 99%

Failure of standard thermodynamics in planck scale black hole system

Nozari

Mehdipour

2009

Chaos, Solitons & Fractals

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The final stage of the black hole evaporation is a matter of debates in the existing literature. In this paper, we consider this problem within two alternative approaches: noncommutative geometry(NCG) and the generalized uncertainty principle(GUP). We compare the results of two scenarios to find a relation between parameters of these approaches. Our results show some extraordinary thermodynamical behavior for Planck size black hole evaporation. These extraordinary behavior may reflect the need for a fractal nonextensive thermodynamics for Planck size black hole evaporation process.

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“…Indeed, the notion of minimal length should quantum mechanically be described as a minimal uncertainty in position measurements. The introduction of this idea has drawn much attention in recent years and many papers have been appeared in the literature to address the effects of GUP on various quantum mechanical systems and phenomena [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]35,36].…”

Section: Introductionmentioning

confidence: 99%

New approach to nonperturbative quantum mechanics with minimal length uncertainty

2012

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The existence of a minimal measurable length is a common feature of various approaches to quantum gravity such as string theory, loop quantum gravity, and black-hole physics. In this scenario, all commutation relations are modified and the Heisenberg uncertainty principle is changed to the so-called Generalized (Gravitational) Uncertainty Principle (GUP). Here, we present a one-dimensional nonperturbative approach to quantum mechanics with minimal length uncertainty relation which implies X ¼ x to all orders and P ¼ p þ 1 3 p 3 to first order of GUP parameter , where X and P are the generalized position and momentum operators and ½x; p ¼ iℏ. We show that this formalism is an equivalent representation of the seminal proposal by Kempf, Mangano, and Mann and predicts the same physics. However, this proposal reveals many significant aspects of the generalized uncertainty principle in a simple and comprehensive form and the existence of a maximal canonical momentum is manifest through this representation. The problems of the free particle and the harmonic oscillator are exactly solved in this GUP framework and the effects of GUP on the thermodynamics of these systems are also presented. Although X, P, and the Hamiltonian of the harmonic oscillator all are formally selfadjoint, the careful study of the domains of these operators shows that only the momentum operator remains self-adjoint in the presence of the minimal length uncertainty. We finally discuss the difficulties with the definition of potentials with infinitely sharp boundaries.

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Generalized uncertainty principle, modified dispersion relations and the early universe thermodynamics

Cited by 76 publications

References 30 publications

Quantum-Spacetime Phenomenology

Quantum-Spacetime Phenomenology

Failure of standard thermodynamics in planck scale black hole system

New approach to nonperturbative quantum mechanics with minimal length uncertainty

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