scholarly journals Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Pasquale Bosso ◽  
Giuseppe Gaetano Luciano
Keyword(s):  
Harmonic Oscillator ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Heisenberg Algebra ◽  
Quantum Field ◽  
Exact Form ◽  
Ladder Operators ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty

AbstractSeveral models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.

scholarly journals Phenomenology of the Pauli exclusion principle violations due to the non-perturbative generalized uncertainty principle

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Andrea Addazi ◽  
Pierluigi Belli ◽  
Rita Bernabei ◽  
Antonino Marcianò ◽  
Homa Shababi
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Pauli Exclusion Principle ◽  
Momentum Conservation ◽  
Exclusion Principle ◽  
Precision Data ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Energy Dependent

Abstract New phenomenological implications of the Generalized Uncertainty Principle (GUP), a modification of the Heisenberg Uncertainty Principle (HUP) are explored in light of constraints arising from underground experiments. An intimate link intertwines the symplectic structure of a theory, which is at the very base of the formulation of the HUP and thus a pillar of quantum mechanics, with the symmetries of space-time and the spin-statistics. Within this wide framework, a large class of non-perturbative GUPs inevitably lead to energy-dependent violations of the total angular momentum conservation rules, and imply hence tiny Pauli Exclusion Principle (PEP) violating transitions. Exotic PEP violating nuclear transitions can be tested, for example, through extremely high precision data provided by the DAMA/LIBRA experiment. We show that several GUP violations are already ruled out up to the quantum gravity Planck scale.

scholarly journals Phenomenological implications of the generalized uncertainty principleThis paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

2009 ◽  
Vol 87 (3) ◽  
pp. 233-240 ◽  
Author(s):  
Saurya Das ◽  
Elias C. Vagenas
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Landau Levels ◽  
Quantum Mechanical ◽  
Reflection And Transmission ◽  
Heisenberg Uncertainty Principle ◽  
Transmission Coefficients ◽  
Heisenberg Uncertainty ◽  
Planck Energy

Various theories of quantum gravity argue that near the Planck scale, the Heisenberg uncertainty principle should be replaced by the so called generalized uncertainty principle (GUP). We show that the GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional to βp4 and β2p6, respectively, where β ∼ 1/(MPlc)2 is the GUP parameter. These terms become important at or above the Planck energy. Considering only the first of these and treating it as a perturbation, we show that the GUP affects the Lamb shift, Landau levels, reflection and transmission coefficients of a potential step and potential barrier, and the current in a scanning tunnel microscope (STM). Although these are too small to be measurable at present, we speculate on the possibility of extracting measurable predictions in the future.

scholarly journals Prediction for the cosmological constant and constraints on SUSY GUTs in resummed quantum gravity

2018 ◽  
Vol 33 (29) ◽  
pp. 1830028
Author(s):  
B. F. L. Ward
Keyword(s):  
General Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Planck Scale ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty

Working in the context of the Planck scale cosmology formulation of Bonanno and Reuter, we use our resummed quantum gravity approach to Einstein’s general theory of relativity to estimate the value of the cosmological constant as [Formula: see text]. We show that SUSY GUT models are constrained by the closeness of this estimate to experiment. We also address various consistency checks on the calculation. In particular, we use the Heisenberg uncertainty principle to remove a large part of the remaining uncertainty in our estimate of [Formula: see text].

scholarly journals Towards Thermodynamics with Generalized Uncertainty Principle

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmed Farag Ali ◽  
Mohamed Moussa
Keyword(s):  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Ideal Gas ◽  
Considerable Change ◽  
Heisenberg Uncertainty Principle ◽  
Ideal Gases ◽  
Quantum Gravity Effect ◽  
Photon Gas ◽  
Heisenberg Uncertainty

Various frameworks of quantum gravity predict a modification in the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Introducing quantum gravity effect makes a considerable change in the density of states inside the volume of the phase space which changes the statistical and thermodynamical properties of any physical system. In this paper we investigate the modification in thermodynamic properties of ideal gases and photon gas. The partition function is calculated and using it we calculated a considerable growth in the thermodynamical functions for these considered systems. The growth may happen due to an additional repulsive force between constitutes of gases which may be due to the existence of GUP, hence predicting a considerable increase in the entropy of the system. Besides, by applying GUP on an ideal gas in a trapped potential, it is found that GUP assumes a minimum measurable value of thermal wavelength of particles which agrees with discrete nature of the space that has been derived in previous studies from the GUP.

Coherent and squeezed states for the 3D harmonic oscillator

2017 ◽  
Vol 31 (03) ◽  
pp. 1750019
Author(s):  
Amel Mazouz ◽  
Mustapha Bentaiba ◽  
Ali Mahieddine
Keyword(s):  
Harmonic Oscillator ◽  
Uncertainty Relation ◽  
Three Dimensional ◽  
Heisenberg Algebra ◽  
Squeezed States ◽  
Ladder Operators ◽  
Compression Effect ◽  
Precise Knowledge ◽  
Generalized Coherent States ◽  
Heisenberg Uncertainty

A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.

scholarly journals A CLASS OF GUP SOLUTIONS IN DEFORMED QUANTUM MECHANICS

2010 ◽  
Vol 19 (12) ◽  
pp. 2003-2009 ◽  
Author(s):  
POURIA PEDRAM
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Uncertainty Principle ◽  
Deformed Algebra ◽  
Heisenberg Uncertainty

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.

Solution of the Dirac equation with exponential-type potential under the GUP

2021 ◽  
Vol 36 (01) ◽  
pp. 2150005
Author(s):  
Lin-Fang Deng ◽  
He-Yao Zhang ◽  
Chao-Yun Long
Keyword(s):  
Dirac Equation ◽  
Uncertainty Principle ◽  
Exponential Type ◽  
Generalized Uncertainty Principle ◽  
Pseudospin Symmetry ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Uvarov Method ◽  
Planck Energy ◽  
Type Potential

In quantum gravity theories, when the scattering energy is comparable to the Planck energy, the usual Heisenberg uncertainty principle breaks down and is replaced by generalized uncertainty principle (GUP). In this paper, the Dirac equation is studied for a single particle with spin and pseudospin symmetry in the presence of GUP, in [Formula: see text] dimensions. For arbitrary wave [Formula: see text], the Dirac equation with multiparameter exponential-type potential is solved by applying the approximation of the centrifugal term and the Nikiforov–Uvarov method. The corresponding energy spectra and eigenvalue function are obtained in the closed form and depend on the GUP parameter. In addition, several interesting cases have been discussed.

scholarly journals EXTENDED UNCERTAINTY PRINCIPLE AND THE GEOMETRY OF (ANTI)-DE SITTER SPACE

2010 ◽  
Vol 25 (20) ◽  
pp. 1697-1703 ◽  
Author(s):  
S. MIGNEMI
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Sitter Spacetime ◽  
Heisenberg Uncertainty ◽  
Sitter Background ◽  
Extended Uncertainty

It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.

scholarly journals Hawking temperature for various kinds of black holes from Heisenberg uncertainty principle

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040004 ◽  
Author(s):  
Fabio Scardigli
Keyword(s):  
Black Holes ◽  
Large Class ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Hawking Temperature ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Classical Physics ◽  
Heisenberg Uncertainty ◽  
Extended Uncertainty

Hawking temperature for a large class of black holes (Schwarzschild, Reissner–Nordström, (Anti) de Sitter, with spherical, toroidal and hyperboloidal topologies) is computed using only laws of classical physics plus the “classical” Heisenberg Uncertainty Principle. This principle is shown to be fully sufficient to get the result, and there is no need to this scope of a Generalized Uncertainty Principle or an Extended Uncertainty Principle.

scholarly journals Tsallis statistics and generalized uncertainty principle

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Giuseppe Gaetano Luciano
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Unruh Effect ◽  
Heisenberg Uncertainty ◽  
Gaussian Statistics ◽  
Non Gaussian ◽  
Effective Description ◽  
Monotonic Relation

AbstractIt has been argued that non-Gaussian statistics provide a natural framework to investigate semiclassical effects in the context of Planck-scale deformations of the Heisenberg uncertainty relation. Here we substantiate this point by considering the Unruh effect as a specific playground. By working in the realm of quantum field theory, we reformulate the derivation of the modified Unruh effect from the generalized uncertainty principle (GUP) in the language of the nonextensive Tsallis thermostatistics. We find a nontrivial monotonic relation between the nonextensivity index q and the GUP deformation parameter $$\beta $$ β , which generalizes an earlier result obtained in quantum mechanics. We then extend our analysis to black hole thermodynamics. We preliminarily discuss our outcome in the broader context of an effective description of Planck-scale gravitational physics based on Tsallis theory.

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