FRACTIONAL ANALYSIS OF WAVE PACKET PROPAGATION AND SOME ASPECTS OF VSL WITH GUP

Fractals ◽  
2008 ◽  
Vol 16 (01) ◽  
pp. 33-42 ◽  
Author(s):  
S. HAMID MEHDIPOUR ◽  
KOUROSH NOZARI ◽  
S. DAVOOD SADATIAN
Keyword(s):  
Wave Packet ◽  
Gordon Equation ◽  
Generalized Uncertainty Principle ◽  
De Sitter ◽  
Modified Dispersion Relation ◽  
Fractional Analysis ◽  
Klein Gordon ◽  
De Sitter Universe ◽  
Klein Gordon Equation ◽  
Wave Packet Broadening

In this paper, we consider the problem of wave packet broadening in the framework of the Generalized Uncertainty Principle (GUP) of quantum gravity. Then we find a fractal Klein-Gordon equation to further analyze the wave packet broadening in a foamy spacetime. We derive a Modified Dispersion Relation (MDR) in the context of GUP which shows an extra broadening due to gravitational induced uncertainty. As a result of these dispersion relations, a generalized Klein-Gordon equation can be obtained. We solve this generalized equation under certain conditions to find both analytical and numerical results. We show that GUP can lead to a variation of the fundamental constants such as speed of light. With this novel properties, we find a time-dependent equation of state for perfect fluid in de Sitter universe and we interpret its physical implications.

scholarly journals On quantum corrections to geodesics in de-Sitter spacetime

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Viacheslav A. Emelyanov
Keyword(s):  
Wave Packet ◽  
Gordon Equation ◽  
Plane Waves ◽  
Hubble Constant ◽  
De Sitter ◽  
Field Mass ◽  
Sitter Spacetime ◽  
Klein Gordon ◽  
De Sitter Universe ◽  
Positive Frequency

AbstractWe find a coordinate-independent wave-packet solution of the massive Klein–Gordon equation with the conformal coupling to gravity in the de-Sitter universe. This solution can locally be represented through the superposition of positive-frequency plane waves at any space-time point, assuming that the scalar-field mass M is much bigger than the de-Sitter Hubble constant H. The solution is also shown to be related to the two-point function in the de-Sitter quantum vacuum. Moreover, we study the wave-packet propagation over cosmological times, depending on the ratio of M and H. In doing so, we find that this wave packet propagates like a point-like particle of the same mass if $$M \ggg H$$ M ⋙ H , but, if otherwise, the wave packet behaves highly non-classically.

scholarly journals FINITE ACTION KLEIN–GORDON SOLUTIONS ON LORENTZIAN MANIFOLDS

2006 ◽  
Vol 03 (07) ◽  
pp. 1349-1357 ◽  
Author(s):  
V. V. KOZLOV ◽  
I. V. VOLOVICH
Keyword(s):  
Mass Spectrum ◽  
Elliptic Equations ◽  
Gordon Equation ◽  
Infinite Family ◽  
De Sitter ◽  
Lorentzian Manifolds ◽  
Klein Gordon ◽  
Finite Action ◽  
Discrete Mass ◽  
Klein Gordon Equation

The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this paper we consider such a problem for the hyperbolic Klein–Gordon equation on Lorentzian manifolds. The investigation could help to answer the question why elementary particles have a discrete mass spectrum. An infinite family of square integrable solutions for the Klein–Gordon equation on the Friedman type manifolds is constructed. These solutions have a discrete mass spectrum and a finite action. In particular the solutions on de Sitter space are investigated.

Electromagnetic interaction with the Klein–Gordon equation in the framework of GUP

2021 ◽  
Vol 18 (12) ◽  
Author(s):  
B. Khosropour
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Uncertainty Principle ◽  
Electric Potential ◽  
Uniform Magnetic Field ◽  
Gordon Equation ◽  
Electromagnetic Interaction ◽  
Generalized Uncertainty Principle ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this work, according to the generalized uncertainty principle, we study the Klein–Gordon equation interacting with the electromagnetic field. The generalized Klein–Gordon equation is obtained in the presence of a scalar electric potential and a uniform magnetic field. Furthermore, we find the relation of the generalized energy–momentum in the presence of a scalar electric potential and a uniform magnetic field separately.

ENTROPY OF SCHWARZSCHILD–de SITTER BLACK HOLE IN NON-THERMAL-EQUILIBRIUM

2001 ◽  
Vol 16 (11) ◽  
pp. 719-723 ◽  
Author(s):  
REN ZHAO ◽  
JUNFANG ZHANG ◽  
LICHUN ZHANG
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Thermal Equilibrium ◽  
Gordon Equation ◽  
Brick Wall ◽  
De Sitter ◽  
Logarithmic Term ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Wall Method

Starting from the Klein–Gordon equation, we calculate the entropy of Schwarzschild–de Sitter black hole in non-thermal-equilibrium by using the improved brick-wall method-membrane model. When taking the proper cutoff in the obtained result, we obtain that both black hole's entropy and cosmic entropy are proportional to the areas of event horizon. We avoid the logarithmic term and stripped term in the original brick-wall method. It offers a new way of studying the entropy of the black hole in non-thermal-equilibrium.

scholarly journals Quantum Gravity Correction to Hawking Radiation of the 2+1-Dimensional Wormhole

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Ganim Gecim ◽  
Yusuf Sucu
Keyword(s):  
Gordon Equation ◽  
Vector Boson ◽  
Generalized Uncertainty Principle ◽  
Tunneling Probability ◽  
Hawking Temperature ◽  
Positive Temperature ◽  
Klein Gordon ◽  
Modified Dirac Equation ◽  
Trapping Horizon ◽  
Klein Gordon Equation

We carry out the Hawking temperature of a 2+1-dimensional circularly symmetric traversable wormhole in the framework of the generalized uncertainty principle (GUP). Firstly, we introduce the modified Klein-Gordon equation of the spin-0 particle, the modified Dirac equation of the spin-1/2 particle, and the modified vector boson equation of the spin-1 particle in the wormhole background, respectively. Given these equations under the Hamilton-Jacobi approach, we analyze the GUP effect on the tunneling probability of these particles near the trapping horizon and, subsequently, on the Hawking temperature of the wormhole. Furthermore, we have found that the modified Hawking temperature of the wormhole is determined by both wormhole’s and tunneling particle’s properties and indicated that the wormhole has a positive temperature similar to that of a physical system. This case indicates that the wormhole may be supported by ordinary (nonexotic) matter. In addition, we calculate the Unruh-Verlinde temperature of the wormhole by using Kodama vectors instead of time-like Killing vectors and observe that it equals to the standard Hawking temperature of the wormhole.

scholarly journals Theoretical Investigation of Subluminal Particles Endowed with Imaginary Mass

2021 ◽  
Author(s):  
Luca Nanni
Keyword(s):  
General Solution ◽  
Wave Packet ◽  
Boundary Conditions ◽  
Theoretical Investigation ◽  
Wave Equations ◽  
Gordon Equation ◽  
Fourier Integral ◽  
Klein Gordon ◽  
Group Velocities ◽  
Klein Gordon Equation

In this article, the general solution of the tachyonic Klein-Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex \omega-plane. In particular, it is proved that under given boundary conditions this solution does not contain any superluminal components. On the basis of this result, we infer that all possible spacelike wave equations describe the dynamics of subluminal particles endowed with imaginary mass. This result is validated for the Chodos equation, used to describe the hypothetical superluminal behaviour of neutrino. In this specific framework, it is proved that the wave packet propagates in spacetime with subluminal group velocities and that for enough small energies it behaves as a localized wave.

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