scholarly journals Position-dependent mass in strong quantum gravitational background fields

2021 ◽  
Author(s):  
Latévi Mohamed Lawson
Keyword(s):  
Quantum Gravity ◽  
Energy Levels ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Gravitational Effect ◽  
Noncommutative Space ◽  
Low Energies ◽  
Background Fields ◽  
Dependent Mass ◽  
Position Dependent Mass

Abstract More recently, we have proposed a set of noncommutative space that describes the quantum gravity at the Planck scale [J. Phys. A: Math. Theor. 53, 115303 (2020)]. The interesting significant result, we found is that, the generalized uncertainty principle induces a maximal measurable length of quantum gravity. This measurement revealed strong quantum gravitational effects at this scale and predicted a detection of gravity particles with low energies. In the present paper, to make evidence this prediction, we study in this space, the dynamics of a particle with position-dependent mass (PDM) trapped in an infinite square well. We show that by increasing the quantum gravitational effect, the PDM of the particle increases and induces deformations of the quantum energy levels. These deformations are more pronounced as one increases the quantum levels allowing, the particle to jump from one state to another with low energies and with high probability densities.

scholarly journals POLYMER GEOMETRY AT PLANCK SCALE AND QUANTUM EINSTEIN EQUATIONS

1996 ◽  
Vol 05 (06) ◽  
pp. 629-648 ◽  
Author(s):  
ABHAY ASHTEKAR
Keyword(s):  
Quantum Gravity ◽  
Planck Scale ◽  
Coarse Graining ◽  
Space Structure ◽  
Einstein Equations ◽  
Hamiltonian Constraint ◽  
Recent Approach ◽  
Canonical Approach ◽  
Background Fields ◽  
Discrete Spectra

Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge equivalent connections. This calculus does not use any background fields (such as a metric) and thus well-suited to a fully non-perturbative treatment of quantum gravity. Using this framework, quantum geometry is examined. Fundamental excitations turn out to be one-dimensional, rather like polymers. Geometrical observables such as areas of surfaces and volumes of regions are purely discrete spectra. Continuum picture arises only upon coarse graining of suitable semi-classical states. Next, regulated quantum diffeomorphism constraints can be imposed in an anomaly-free fashion and the space of solutions can be given a natural Hilbert space structure. Progress has also been made on the quantum Hamiltonian constraint in a number of directions. In particular, there is a recent approach based on a generalized .Wick transformation which maps solutions to the Euclidean quantum constraints to those of the Lorentzian theory. These developments are summarized. Emphasis is on conveying the underlying ideas and overall pictures rather than technical details.

SOLUTION OF THE DIRAC EQUATION WITH POSITION-DEPENDENT MASS IN A COULOMB AND SCALAR FIELDS IN A CONICAL SPACETIME

2013 ◽  
Vol 28 (31) ◽  
pp. 1350137 ◽  
Author(s):  
GEUSA DE A. MARQUES ◽  
V. B. BEZERRA ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Cosmic String ◽  
Relativistic Particle ◽  
Energy Levels ◽  
Scalar Potential ◽  
Scalar Fields ◽  
The Self ◽  
Dependent Mass ◽  
Scalar Potentials ◽  
Position Dependent Mass

We consider the problem of a relativistic particle with position-dependent mass in the presence of a Coulomb and a scalar potentials in the background spacetime generated by a cosmic string. The scalar potential arises from the self-interaction potential which is induced by the conical geometry of the spacetime under consideration. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle. The behavior of the energy levels on the parameters associated with the presence of the cosmic string and with the fact that the mass of the particle depends on its position is also analyzed.

Klein–Gordon oscillator with position-dependent mass in the rotating cosmic string spacetime

2018 ◽  
Vol 33 (04) ◽  
pp. 1850025 ◽  
Author(s):  
Bing-Qian Wang ◽  
Zheng-Wen Long ◽  
Chao-Yun Long ◽  
Shu-Rui Wu
Keyword(s):  
Magnetic Field ◽  
Cosmic String ◽  
Energy Levels ◽  
Homogeneous Magnetic Field ◽  
Spinless Particle ◽  
Klein Gordon ◽  
Coulomb Type ◽  
Dependent Mass ◽  
String Background ◽  
Position Dependent Mass

A spinless particle coupled covariantly to a uniform magnetic field parallel to the string in the background of the rotating cosmic string is studied. The energy levels of the electrically charged particle subject to the Klein–Gordon oscillator are analyzed. Afterwards, we consider the case of the position-dependent mass and show how these energy levels depend on the parameters in the problem. Remarkably, it shows that for the special case, the Klein–Gordon oscillator coupled covariantly to a homogeneous magnetic field with the position-dependent mass in the rotating cosmic string background has the similar behaviors to the Klein–Gordon equation with a Coulomb-type configuration in a rotating cosmic string background in the presence of an external magnetic field.

scholarly journals Modified Newton's Law of Gravitation due to Minimal Length in Quantum Gravity

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmed Farag Ali ◽  
A. Tawfik
Keyword(s):  
Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Recent Theory ◽  
Entropic Force ◽  
Doubly Special Relativity ◽  
Newton's Law ◽  
Newton’S Law ◽  
Area Law

A recent theory about the origin of the gravity suggests that the gravity is originally an entropic force. In this work, we discuss the effects of generalized uncertainty principle (GUP) which is proposed by some approaches to quantum gravity such as string theory, black hole physics, and doubly special relativity theories (DSR), on the area law of the entropy. This leads to aarea-type correction to the area law of entropy which implies that the number of bitsNis modified. Therefore, we obtain a modified Newton’s law of gravitation. Surprisingly, this modification agrees with different sign with the prediction of Randall-Sundrum II model which contains one uncompactified extra dimension. Furthermore, such modification may have observable consequences at length scales much larger than the Planck scale.

scholarly journals BUILDING A CASE FOR A PLANCK-SCALE-DEFORMED BOOST ACTION: THE PLANCK-SCALE PARTICLE-LOCALIZATION LIMIT

2005 ◽  
Vol 14 (12) ◽  
pp. 2167-2180 ◽  
Author(s):  
GIOVANNI AMELINO-CAMELIA
Keyword(s):  
Quantum Gravity ◽  
Semiclassical Approximation ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Doubly Special Relativity ◽  
Logarithmic Corrections ◽  
Additional Challenge ◽  
Scale Particle ◽  
Particle Localization

"Doubly-special relativity" (DSR), the idea of a Planck-scale Minkowski limit that is still a relativistic theory, but with both the Planck scale and the speed-of-light scale as nontrivial relativistic invariants, was proposed as a physics intuition for several scenarios which may arise in the study of the quantum-gravity problem, but most DSR studies focused exclusively on the search of formalisms for the description of a specific example of such a Minkowski limit. A novel contribution to the DSR physics intuition came from a recent paper by Smolin suggesting that the emergence of the Planck scale as a second nontrivial relativistic invariant might be inevitable in quantum gravity, relying only on some rather robust expectations concerning the semiclassical approximation of quantum gravity. Here, we attempt to strengthen Smolin's argument by observing that an analysis of some independently-proposed Planck-scale particle-localization limits, such as the "Generalized Uncertainty Principle" often attributed to string theory in the literature, also suggests that the emergence of a DSR Minkowski limit might be inevitable. We discuss a possible link between this observation and recent results on logarithmic corrections to the entropy-area black-hole formula, and observe that both the analysis reported here and Smolin's analysis appear to suggest that the examples of DSR Minkowski limits for which a formalism has been sought in the literature might not be sufficiently general. We also stress that, as we now contemplate the hypothesis of a DSR Minkowski limit, there is an additional challenge for those in the quantum-gravity community attributing to the Planck length the role of "fundamental length scale."

scholarly journals Effect of Generalized Uncertainty Principle on Main-Sequence Stars and White Dwarfs

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Moussa
Keyword(s):  
Quantum Gravity ◽  
Uncertainty Principle ◽  
White Dwarfs ◽  
Main Sequence ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Main Sequence Stars ◽  
Emden Equation ◽  
Astrophysical Objects ◽  
Applicable Range

This paper addresses the effect of generalized uncertainty principle, emerged from different approaches of quantum gravity within Planck scale, on thermodynamic properties of photon, nonrelativistic ideal gases, and degenerate fermions. A modification in pressure, particle number, and energy density are calculated. Astrophysical objects such as main-sequence stars and white dwarfs are examined and discussed as an application. A modification in Lane-Emden equation due to a change in a polytropic relation caused by the presence of quantum gravity is investigated. The applicable range of quantum gravity parameters is estimated. The bounds in the perturbed parameters are relatively large but they may be considered reasonable values in the astrophysical regime.

scholarly journals A novel mechanism for probing the Planck scale

2021 ◽  
Author(s):  
Saurya Das ◽  
Sujoy Modak
Keyword(s):  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Relativistic Correction ◽  
Leading Order ◽  
Mean Velocity ◽  
Important Improvement ◽  
Gravity Effects ◽  
Time Required

Abstract The Planck or the quantum gravity scale, being $16$ orders of magnitude greater than the electroweak scale, is often considered inaccessible by current experimental techniques. However, it was shown recently by one of the current authors that quantum gravity effects via the Generalized Uncertainty Principle affects the time required for free wavepackets to double their size, and this difference in time is at or near current experimental accuracies [1,2]. In this work, we make an important improvement over the earlier study, by taking into account the leading order relativistic correction, which naturally appears in the sytems under consideration, due to the significant mean velocity of the travelling wavepackets. Our analysis shows that although the relativistic correction adds nontrivial modifications to the results of [1,2], the earlier claims remain intact and are in fact strengthened. We explore the potential for these results being tested in the laboratory.

scholarly journals EFFECT OF THE GENERALIZED UNCERTAINTY PRINCIPLE ON COMPACT STARS

2013 ◽  
Vol 22 (05) ◽  
pp. 1350020 ◽  
Author(s):  
AHMED FARAG ALI ◽  
ABDEL NASSER TAWFIK
Keyword(s):  
String Theory ◽  
Thermodynamic Properties ◽  
Quantum Gravity ◽  
Special Relativity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Compact Stars ◽  
Doubly Special Relativity ◽  
Heisenberg Principle

Based on the generalized uncertainty principle (GUP), proposed by some approaches to quantum gravity such as string theory and doubly special relativity theories, we investigate the effect of GUP on the thermodynamic properties of compact stars with two different components. We note that the existence of quantum gravity correction tends to resist the collapse of stars if the GUP parameter α is taking values between Planck scale and electroweak scale. Comparing with approaches, it is found that the radii of compact stars become smaller relative to the cases utilizing standard Heisenberg principle. Increasing energy almost exponentially decreases the radii of compact stars.

scholarly journals Thermodynamics of Ideal Gas at Planck Scale with Strong Quantum Gravity Measurement

2021 ◽  
Author(s):  
Latevi Mohamed Lawson
Keyword(s):  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Free Particle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Ideal Gas ◽  
Minimal Length ◽  
Maximal Length ◽  
Gravity Measurement ◽  
Thermodynamic Quantities

Abstract More recently in J. Phys. A: Math. Theor. 53, 115303 (2020), we have introduced a set of noncommutative algebra that describes the space-time at the Planck scale. The interesting significant result we found is that the generalized uncertainty principle induced a maximal length of quantum gravity which has different physical implications to the one of generalized uncertainty principle with minimal length. The emergence of a maximal length in this theory revealed strong quantum gravitational effects at this scale and predicted the detection of gravity particles with low energies. To make evidence of these predictions, we study the dynamics of a free particle confined in an infinite square well potential in one dimension of this space. Since the effects of quantum gravity are strong in this space, we show that the energy spectrum of this system is weakly proportional to the ordinary one of quantum mechanics free of the theory of gravity. The states of this particle exhibit proprieties similar to the standard coherent states which are consequences of quantum fluctuation at this scale. Then, with the spectrum of this system at hand, we analyze the thermodynamic quantities within the canonical and micro-canonical ensembles of an ideal gas made up of N indistinguishable particles at the Planck scale. The results show a complete consistency between both statistical descriptions. Furthermore, a comparison with the results obtained in the context of minimal length scenarios and black hole theories indicates that the maximal length in this theory induces logarithmic corrections of deformed parameters which are consequences of a strong quantum gravitational effect.

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.

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