RELATIVISTIC PARTICLE IN ELECTROMAGNETIC FIELDS WITH A GENERALIZED UNCERTAINTY PRINCIPLE

2012 ◽  
Vol 27 (15) ◽  
pp. 1250080 ◽  
Author(s):  
M. MERAD ◽  
F. ZEROUAL ◽  
M. FALEK
Keyword(s):  
Electromagnetic Field ◽  
Small Parameter ◽  
Uncertainty Principle ◽  
Relativistic Particle ◽  
Generalized Uncertainty Principle ◽  
Limit Case ◽  
Energy Eigenvalues ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Uniform Electromagnetic Field

In this paper, we propose to solve the relativistic Klein–Gordon and Dirac equations subjected to the action of a uniform electromagnetic field with a generalized uncertainty principle in the momentum space. In both cases, the energy eigenvalues and their corresponding eigenfunctions are obtained. The limit case is then deduced for a small parameter of deformation.

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.

scholarly journals Discreteness of Curved Spacetime from GUP

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Ahmad Adel Abutaleb
Keyword(s):  
Dirac Equation ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Curved Spacetime ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Heisenberg's Uncertainty Principle ◽  
Area And Volume

Diverse theories of quantum gravity expect modifications of the Heisenberg's uncertainty principle near the Planck scale to a so-called Generalized uncertainty principle (GUP). It was shown by some authors that the GUP gives rise to corrections to the Schrodinger , Klein-Gordon, and Dirac equations. By solving the GUP corrected equations, the authors arrived at quantization not only of energy but also of box length, area, and volume. In this paper, we extend the above results to the case of curved spacetime (Schwarzschild metric). We showed that we arrived at the quantization of space by solving Dirac equation with GUP in this metric.

scholarly journals Hawking radiation from cubic and quartic black holes via tunneling of GUP corrected scalar and fermion particles

2019 ◽  
Vol 34 (09) ◽  
pp. 1950057 ◽  
Author(s):  
Wajiha Javed ◽  
Rimsha Babar ◽  
Ali Övgün
Keyword(s):  
Black Holes ◽  
Hawking Radiation ◽  
Generalized Uncertainty Principle ◽  
Hawking Temperature ◽  
Jacobi Method ◽  
Dirac Equations ◽  
Tensor Theory ◽  
Klein Gordon ◽  
The Given ◽  
Do So

We analyze the effect of the generalized uncertainty principle (GUP) on the Hawking radiation from the hairy black hole in U(1) gauge-invariant scalar–vector–tensor theory by utilizing the semiclassical Hamilton–Jacobi method. To do so, we evaluate the tunneling probabilities and Hawking temperature for scalar and fermion particles for the given spacetime of the black holes with cubic and quartic interactions. For this purpose, we utilize the modified Klein–Gordon equation for the Boson particles and then Dirac equations for the fermion particles, respectively. Next, we examine that the Hawking temperature of the black holes do not depend on the properties of tunneling particles. Moreover, we present the corrected Hawking temperature of scalar and fermion particles which look similar in both interactions, but there are different mass and momentum relationships for scalar and fermion particles in cubic and quartic interactions.

scholarly journals Relativistic particle in a box: Klein–Gordon versus Dirac equations

2018 ◽  
Vol 39 (2) ◽  
pp. 025401 ◽  
Author(s):  
Pedro Alberto ◽  
Saurya Das ◽  
Elias C Vagenas
Keyword(s):  
Relativistic Particle ◽  
Dirac Equations ◽  
Klein Gordon

QUANTUM EFFECTS IN A COMBINATION OF A CONSTANT UNIFORM FIELD AND A PLANE WAVE FIELD

1991 ◽  
Vol 06 (25) ◽  
pp. 4437-4489 ◽  
Author(s):  
D.M. GITMAN ◽  
M.D. NOSKOV ◽  
SH. M. SHVARTSMAN
Keyword(s):  
Plane Wave ◽  
Wave Field ◽  
Quantum Electrodynamics ◽  
Quantum Effects ◽  
Uniform Field ◽  
Dirac Equations ◽  
Radiative Processes ◽  
Klein Gordon ◽  
Plane Wave Field ◽  
Uniform Electromagnetic Field

Quantum effects are considered in the external field, which is a superposition of a constant uniform electromagnetic field and a plane wave field. The complete and orthonormal sets of solutions to the Klein-Gordon and Dirac equations are constructed for this field. The probabilities of scattering and pair creation are calculated. The representations of various Green functions, which are used in quantum electrodynamics with unstable vacuum, are obtained. The radiative processes are explored for the field under consideration.

Quantum gravity effect on the tunneling particles from Warped-AdS3 black hole

2018 ◽  
Vol 33 (28) ◽  
pp. 1850164 ◽  
Author(s):  
Ganim Gecim ◽  
Yusuf Sucu
Keyword(s):  
Black Hole ◽  
Angular Velocity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Scalar Particle ◽  
Hawking Temperature ◽  
Dirac Equations ◽  
Inner Horizon ◽  
Quantum Gravity Effect ◽  
Klein Gordon

In this study, using the Hamilton–Jacobi approach, we investigated the Hawking temperature of the (2 + 1)-dimensional Warped-AdS3 black hole by considering the generalized uncertainty principle (GUP) effect. In this connection, we calculated quantum mechanical tunneling probabilities of the scalar spin-0 and Dirac spin-[Formula: see text] particles from the black hole by using the modified Klein–Gordon and Dirac equations, respectively. Then, we observed that the Hawking temperature of the black hole depends not only on radius and angular velocity of the outer horizon of the black hole, but also on the angular velocity of the inner horizon of the black hole and the total angular momentum, energy and mass of a tunneling particle. In this case, the Hawking radiation of Dirac particle is different from that of the scalar particle. Moreover, this situation shows that the Hawking temperature calculated under the GUP may give us information about which sort of particle is tunneling. And, the direct dependence of the Hawking temperature to the inner horizon’s angular velocity makes the effect of the Chandrasekhar–Friedman–Schutz (CFS) mechanism more clear in the black hole physics.

scholarly journals Effects of extended uncertainty principle on the relativistic Coulomb potential

2021 ◽  
Vol 36 (03) ◽  
pp. 2150018
Author(s):  
B. Hamil ◽  
M. Merad ◽  
T. Birkandan
Keyword(s):  
Uncertainty Principle ◽  
Coulomb Potential ◽  
State Energy ◽  
Bound State ◽  
Wave Functions ◽  
De Sitter ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Relativistic Coulomb ◽  
Extended Uncertainty

The relativistic bound-state energy spectrum and the wave functions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein–Gordon and Dirac equations are solved analytically to obtain the results. The electron energies of hydrogen-like atoms are studied numerically.

scholarly journals Penetration of non-uniform electromagnetic field into conducting body

2021 ◽  
pp. 43-53
Author(s):  
Yu. M. Vasetsky
Keyword(s):  
Electromagnetic Field ◽  
External Field ◽  
Small Parameter ◽  
Penetration Depth ◽  
Half Space ◽  
Skin Effect ◽  
Asymptotic Series ◽  
Uniform Field ◽  
Impedance Boundary ◽  
Uniform Electromagnetic Field

The study is based on the exact analytical solution for the general conjugation problem of three-dimensional quasi-stationary field at a flat interface between dielectric and conducting media. It is determined that non-uniform electromagnetic field always decreases in depth faster than uniform field. The theoretical conclusion is confirmed by comparing the results of analytical and numerical calculations. The concept of strong skin effect is extended to the case when penetration depth is small not only compare to the characteristic body size, but also when the ratio of the penetration depth to the distance from the surface of body to the sources of the external field is small parameter. For strong skin effect in its extended interpretation, the influence of external field non-uniformity to electromagnetic field formation both at the interface between dielectric and conducting media and to the law of decrease field in conducting half-space is analyzed. It is shown, at the interface the expressions for the electric and magnetic intensities in the form of asymptotic series in addition to local field values of external sources contain their derivatives with respect to the coordinate perpendicular to the interface. The found expressions made it possible to generalize the approximate Leontovich impedance boundary condition for diffusion of non-uniform field into conducting half-space. The difference between the penetration law for the non-uniform field and the uniform one takes place in the terms of the asymptotic series proportional to the small parameter to the second power and to the second derivative with respect to the vertical coordinate from the external magnetic field intensity at the interface.

Quantum gravity corrections to tunneling of spin-1/2 fermions from Kerr–Newman Black Hole

2021 ◽  
pp. 2150123
Author(s):  
Aheibam Keshwarjit Singh ◽  
Irom Ablu Meitei ◽  
Telem Ibungochouba Singh ◽  
Kangujam Yugindro Singh
Keyword(s):  
Black Hole ◽  
Electromagnetic Field ◽  
Dirac Equation ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Hawking Temperature ◽  
Curved Space ◽  
Gravity Effects ◽  
Newman Black Hole

In this paper, we solve the Dirac Equation in curved space–time, modified by the generalized uncertainty principle, in the presence of an electromagnetic field. Using this, we study the tunneling of [Formula: see text]-spin fermions from Kerr–Newman black hole. Corrections to the Hawking temperature and entropy of the black hole due to quantum gravity effects are also discussed.

Spinless Particle in a Magnetic Field Under Minimal Length Scenario

2016 ◽  
Vol 71 (6) ◽  
pp. 481-485 ◽  
Author(s):  
S.M. Amirfakhrian
Keyword(s):  
Magnetic Field ◽  
Numerical Method ◽  
Uncertainty Principle ◽  
Gordon Equation ◽  
Minimal Length ◽  
Spinless Particle ◽  
Energy Eigenvalues ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractIn this article, we studied the Klein–Gordon equation in a generalised uncertainty principle (GUP) framework which predicts a minimal uncertainty in position. We considered a spinless particle in this framework in the presence of a magnetic field, applied in the z-direction, which varies as ${1 \over {{x^2}}}.$ We found the energy eigenvalues of this system and also obtained the correspounding eigenfunctions, using the numerical method. When GUP parameter tends to zero, our solutions were in agreement with those obtained in the absence of GUP.

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