Discreteness of Space from GUP II: Relativistic Wave Equations

Abstract

Various theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). In some recent papers, we showed that the GUP gives rise to corrections to the Schrodinger equation, which in turn affect all quantum mechanical Hamiltonians. In particular, by applying it to a particle in a one dimensional box, we showed that the box length must be quantized in terms of a fundamental length (which could be the Planck length), which we interpreted as a signal of fundamental discreteness of space itself. In this paper, we extend the above results to a relativistic particle in a rectangular as well as a spherical box, by solving the GUP-corrected Klein-Gordon and Dirac equations, and for the latter, to two and three dimensions. We again arrive at quantization of box length, area and volume and an indication of the fundamentally grainy nature of space. We discuss possible implications.

v1:8 pages, revtex4, no figures, to appear in Phys. Lett. B; v2: version to match published version in PLB, corrections in ERRATUM included

References in corpus (4)

• Universality of Quantum Gravity Corrections
• Discreteness of Space from the Generalized Uncertainty Principle
• Natural extension of the Generalised Uncertainty Principle
• Berry Phase Effects in the dynamics of Dirac Electrons in Doubly Special Relativity Framework

Cited by in corpus (160)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Minimal Length Scale Scenarios for Quantum Gravity
• A proposal for testing Quantum Gravity in the lab
• Generalized Uncertainty Principle: Approaches and Applications
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum
• Minimal length, maximal momentum and Hilbert space representation of quantum mechanics
• Review on Generalized Uncertainty Principle
• The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications
• Constraining the generalized uncertainty principle with the gravitational wave event GW150914
• Minimal Length in Quantum Gravity, Equivalence Principle and Holographic Entropy Bound
• Natural Cutoffs and Quantum Tunneling from Black Hole Horizon
• Planck scale effects on some low energy quantum phenomena
• Generalized uncertainty principle and black hole thermodynamics
• No Existence of Black Holes at LHC Due to Minimal Length in Quantum Gravity
• Black Hole Entropy and the Modified Uncertainty Principle: A heuristic analysis
• 30 years in: Quo vadis generalized uncertainty principle?
• Constraints on the Generalized Uncertainty Principle from Black Hole Thermodynamics
• Modified Dispersion Relation, Photon's Velocity, and Unruh Effect
• Semiclassical corrections to black hole entropy and the generalized uncertainty principle
• Thermodynamics and Shadows of GUP-corrected Black Holes with Topological Defects in Bumblebee Gravity
• Quantum gravity effect on the Hawking radiation of charged rotating BTZ black hole
• Minimal length, maximal momentum and the entropic force law
• More on the initial singularity problem in gravity's rainbow cosmology
• Generalized Uncertainty Principle and Angular Momentum
• Generalized Dirac structure beyond the linear regime in graphene
• Black Hole Entropy with minimal length in Tunneling formalism
• On the Minimal Length Uncertainty Relation and the Foundations of String Theory
• Effect of the Generalized Uncertainty Principle on Post-Inflation Preheating
• Amplified transduction of Planck-scale effects using quantum optics
• The Most General Form of Deformation of the Heisenberg Algebra from the Generalized Uncertainty Principle
• Cosmological Constant from a Deformation of the Wheeler-DeWitt Equation
• Scalar field cosmology modified by the Generalized Uncertainty Principle
• Time Crystals from Minimum Time Uncertainty
• Baryon Asymmetry from the Generalized Uncertainty Principle
• Incorporation of Generalized Uncertainty Principle into Lifshitz Field Theories
• Quantum Black Hole and the Modified Uncertainty Principle
• The Path Integral Quantization corresponding to the Deformed Heisenberg Algebra
• Impacts of Generalized Uncertainty Principle on Black Hole Thermodynamics and Salecker-Wigner Inequalities
• Position and Momentum Uncertainties of the Normal and Inverted Harmonic Oscillators under the Minimal Length Uncertainty Relation
• Relativistic particle in a three-dimensional box
• Emergence of Cosmic Space and Minimal Length in Quantum Gravity
• Scale--dependent Hayward black hole and the generalized uncertainty principle
• Towards a Cosmology with Minimal Length and Maximal Energy
• Singular inverse square potential in coordinate space with a minimal length
• Effects of quantum gravity on the inflationary parameters and thermodynamics of the early universe
• Quasinormal modes and thermodynamic properties of GUP-corrected Schwarzschild black hole surrounded by quintessence
• Discreteness of Space from GUP in a Weak Gravitational Field
• Kratzer's molecular potential in quantum mechanics with a generalized uncertainty principle
• Deformation of the Wheeler-DeWitt Equation
• Effect of the modified Heisenberg algebra on the Black hole thermodynamics
• Do the Modified Uncertainty Principle and Polymer Quantization predict same physics?
• Effects of the Generalized Uncertainty Principle on Compact Stars
• Effects of GUP in Quantum Cosmological Perfect Fluid Models
• Maximal momentum GUP leads to quadratic gravity
• The Generalized Uncertainty Principle and the Friedmann equations
• On the (2+1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty
• Lorentz Invariance Violation and Generalized Uncertainty Principle
• Harmonic oscillator with minimal length, minimal momentum, and maximal momentum uncertainties in SUSYQM framework
• Quantum gravity correction to Hawking radiation of the 2+1 dimensional wormhole
• Planck scale effects on the stochastic gravitational wave background generated from cosmological hadronization transition: A qualitative study
• Minimal Length and the Quantum Bouncer: A Nonperturbative Study
• Emergent universe in theories with natural UV cutoffs
• Short distance modification of the quantum virial theorem
• Exact Ultra Cold Neutrons' Energy Spectrum in Gravitational Quantum Mechanics
• Quantum theory of the Generalised Uncertainty Principle
• The Constraints and Spectra of a Deformed Quantum Mechanics
• Black Hole Corrections due to Minimal Length and Modified Dispersion Relation
• Lagrangian Formulation of a Magnetostatic Field in the Presence of a Minimal Length Scale Based on the Kempf Algebra
• Primordial Power Spectra of Cosmological Fluctuations with Generalized Uncertainty Principle and Maximum Length Quantum Mechanics
• Discreteness of Space from GUP in Strong Gravitational Fields
• Dilaton cosmology and the Modified Uncertainty Principle
• Quantum Gravity Effect on the Tunneling Particles from 2+1 dimensional New-type Black Hole
• Universality of minimal length
• Effects of the Modified Uncertainty Principle on the Inflation Parameters
• GUP-corrected black holes: Thermodynamic properties, evaporation time and shadow constraint from EHT Observations of M87* and Sgr A*
• Modified Newton's Law of Gravitation Due to Minimal Length in Quantum Gravity
• Gravitational effects on the Heisenberg Uncertainty Principle: a geometric approach
• New higher-order generalized uncertainty principle: Applications
• Thermostatistics of the Polymeric Ideal Gas
• Generalized relativistic harmonic oscillator in minimal length quantum mechanics
• Indirect Probe of Quantum Gravity using Molecular Wave-packets
• Relativistic particle in a box: Klein-Gordon vs Dirac Equations
• Generalized uncertainty principle in graphene
• Probing Planck Scale Spacetime By Cavity Opto-Atomic ${}^{87}$Rb Interferometry
• Pseudoharmonic oscillator in quantum mechanics with a minimal length
• Minimal length, maximal momentum and stochastic gravitational waves spectrum generated from cosmological QCD phase transition
• Implication of geodesic equation in Generalized Uncertainty Principle framework
• On the viability of Planck scale cosmology with quartessence
• The three "layers" of graphene monolayer and their analog generalized uncertainty principles
• Maximally localized states and quantum corrections of black hole thermodynamics in the framework of a new generalized uncertainty principle
• Discreteness of time in the evolution of the universe
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Quantum gravitational signatures in next-generation gravitational wave detectors
• The minimal length uncertainty and the nonextensive thermodynamics
• Effects of discrete topology on quantum transport across a graphene $n-p-n$ junction: A quantum gravity analogue
• Turning graphene into a lab for noncommutativity
• The tunneling radiation of a black hole with a $f(R)$ global monopole under generalized uncertainty principle
• The fragmentation instability of a black hole with $f(R)$ global monopole under GUP
• Dimension of quantum channel of radiation in pure Lovelock black holes
• On the Physics of the Minimal Length: The Question of Gauge Invariance
• On the reformulation of Thomas-Fermi model to make it compatible to the Planck-scale
• A framework for nonrelativistic isotropic models based on generalized uncertainty principles
• Neutrino Decoherence from Generalised Uncertainty
• Quantum Gravity effect on the Quark-Gluon Plasma
• Deformed Gazeau-Klauder Schrödinger-Cat States with Modified Commutation Relations
• Massless Charged Particles Tunneling Radiation from a RN-dS Horizon and the Linear and Quadratic GUP
• Quantum phase transitions of the Dirac oscillator in the Anti-Snyder model
• Thermodynamics of black holes and the symmetric generalized uncertainty principle
• Planck-Scale Corrections to Friedmann Equation
• Radiation of Charged Black Holes and Modified Dispersion Relation
• Two-body Dirac equation in DSR: results for fermion-antifermion pairs
• Cosmology from quantum potential in a system of oscillating branes
• Discreteness Of Curved Space-Time From GUP
• A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
• Measurable Maximal Energy and Minimal Time Interval
• Non-Relativistic Anti-Snyder Model and Some Applications
• Linear-Quadratic GUP and Thermodynamic Dimensional Reduction
• Generalized uncertainty principle and neutrino phenomenology
• Photon velocity, power spectrum in Unruh effect with modified dispersion relation
• Generalized Uncertainty Principle and Quantum Gravity Phenomenology
• Thermodynamic phase transition of a Schwarzschild black hole with global monopole under GUP
• Relativistic Approach to the Hydrogen Atom in a Minimal Length Scenario
• Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
• Birth of the GUP and its effect on the entropy of the Universe in Lie-$N$-algebra
• Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
• Generalized Uncertainty Principle, Modified Dispersion Relation and Barrier penetration by a Dirac particle
• Loop Quantum Cosmology with a noncommutative quantum deformed photon gas
• Entropy Bound with Generalized Uncertainty Principle in General Dimensions
• Discriminating between different modified dispersion relations from gamma-ray observations
• Relativistic Generalized Uncertainty Principle and Its Implications
• Transition Rate and the Photoelectric Effect in the Presence of a Minimal Length
• Derivation of the deformed Heisenberg algebra from discrete spacetime
• Squeezing of light from Planck-scale physics
• Remark on Remnant and Residue Entropy with GUP
• A Note on Coherent States with Quantum Gravity Effects
• New Non-commutative and Higher Derivatives Quantum Mechanics from GUPs
• Thermodynamic modifications to Bardeen black holes surrounded by quintessence based on the new higher order GUP
• Quantum tunneling driven by quintessence and the role of GUP
• Lorentz Force and Ponderomotive Force in the Presence of a Minimal Length
• The tunneling radiation of Kehagias-Sfetsos black hole under generalized uncertainty principle
• Effective information bounds in modified quantum mechanics
• Quantum Gravity Corrections to the Mean Field Theory of Nucleons
• (2 +1)-dimensional Duffin-Kemmer-Petiau oscillator under a magnetic field in the presence of a minimal length in the noncommutative space
• Effects of underlying topology on quantum state discrimination
• Particle in a cavity in one-dimensional bandlimited quantum mechanics
• Deformation of Nanowires and Nanotubes
• Lattice oscillator model, scattering theory and a many-body problem
• Ideal Quantum Gases with Planck Scale Limitations
• The Extended Uncertainty Principle from a Projector-Valued Measurement Perspective
• Thermomagnetic Ettingshausen-Nernst effect in tachocline, magnetic reconnection phenomenon in lower layers, axion mechanism of solar luminosity variations, coronal heating problem solution and mechanism of ADM variations around BH
• Analysis of black hole thermodynamics under Generalized uncertainty principle from the doubly special relativity
• The Quark-Gluon Plasma Equation of State and The Generalized Uncertainty Principle
• One-dimension quantum systems in the framework of the most general deformation GUP form
• Maximally localized states and quantum corrections of black hole thermodynamics in the extreme case with an improved exponential GUP
• Minimal length implications on the Hartree-Fock theory
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation
• The instability of a black hole with $f(R)$ global monopole under extended uncertainty principle
• Thermodynamics of Einstein-Gauss-Bonnet Black Holes under the Generalized Uncertainty Principle
• Angular Momentum Operators from Quantized SO(3)