Phenomenological Implications of the Generalized Uncertainty Principle

Abstract

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 βp^4 and β^2 p^6 respectively, where β\sim 1/(M_{Pl}c)^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.

7 pages. Based on talk by S. Das at Theory Canada 4, Montreal, 4 June, 2008. To be published in the Canadian Journal of Physics

References in corpus (1)

• Universality of Quantum Gravity Corrections

Cited by in corpus (139)

• Minimal Length Scale Scenarios for Quantum Gravity
• Discreteness of Space from the Generalized Uncertainty Principle
• A proposal for testing Quantum Gravity in the lab
• Discreteness of Space from GUP II: Relativistic Wave Equations
• Generalized Uncertainty Principle: Approaches and Applications
• 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
• Constraining the generalized uncertainty principle with the gravitational wave event GW150914
• Minimal Length in Quantum Gravity, Equivalence Principle and Holographic Entropy Bound
• Planck scale effects on some low energy quantum phenomena
• Minimal Length and Bouncing Particle Spectrum
• 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
• Quasinormal modes and shadow of a Schwarzschild black hole with GUP
• Relativistic Generalized Uncertainty Principle
• A class of GUP solutions in deformed quantum mechanics
• 30 years in: Quo vadis generalized uncertainty principle?
• Modified Dispersion Relation, Photon's Velocity, and Unruh Effect
• GUP parameter and black hole temperature
• Semiclassical corrections to black hole entropy and the generalized uncertainty principle
• On the modification of Hamiltonians' spectrum in gravitational quantum mechanics
• Cosmological Horizons, Uncertainty Principle and Maximum Length Quantum Mechanics
• Generalized Uncertainty Principle and Angular Momentum
• Minimal length, maximal momentum and the entropic force law
• Effect of the Generalized Uncertainty Principle on Post-Inflation Preheating
• Rigorous Hamiltonian and Lagrangian analysis of classical and quantum theories with minimal length
• On the Minimal Length Uncertainty Relation and the Foundations of String Theory
• Planck scale Corrections to the Harmonic Oscillator, Coherent and Squeezed States
• Cosmological Constant from a Deformation of the Wheeler-DeWitt Equation
• Upper bound on the GUP parameter using the black hole shadow
• Quantum-corrected scattering and absorption of a Schwarzschild black hole with GUP
• Derivations of group rings
• Geodesic equation in $k$-Minkowski spacetime
• Generalized uncertainty principle and Asymptotic Safe gravity
• Baryon Asymmetry from the Generalized Uncertainty Principle
• Quantum Black Hole and the Modified Uncertainty Principle
• Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length
• Generalized uncertainty principle or curved momentum space?
• Minimal Length Effects on Quantum Cosmology and Quantum Black Hole Models
• Position and Momentum Uncertainties of the Normal and Inverted Harmonic Oscillators under the Minimal Length Uncertainty Relation
• Scale--dependent Hayward black hole and the generalized uncertainty principle
• Linear and Quadratic GUP, Liouville Theorem, Cosmological Constant, and Brick Wall Entropy
• Free particle wavefunction in light of the minimum-length deformed quantum mechanics and some of its phenomenological implications
• Quantum Gravity Corrections and Entropy at the Planck time
• Towards a Cosmology with Minimal Length and Maximal Energy
• Cosmological constraints on the Generalized Uncertainty Principle from modified Friedmann equations
• Bounds on GUP parameters from GW150914 and GW190521
• Hubble tension bounds the GUP and EUP parameters
• $\kappa$-deformed Dirac Equation
• 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
• Quantum Wells and the Generalized Uncertainty Principle
• Maximal momentum GUP leads to quadratic gravity
• On the (2+1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty
• The Generalized Uncertainty Principle and the Friedmann equations
• Lorentz Invariance Violation and Generalized Uncertainty Principle
• Path Integral for non-relativistic Generalized Uncertainty Principle corrected Hamiltonian
• Effect of Generalized Uncertainty Principle on Main-Sequence Stars and White Dwarfs
• The Minimal Length and the Quantum Partition Functions
• The GUP and quantum Raychaudhuri equation
• Quantum theory of the Generalised Uncertainty Principle
• Remnant mass and entropy of black holes and modified uncertainty principle
• Noncommutative correction to the entropy of BTZ black hole with GUP
• Constraining the Generalized Uncertainty Principle with the light twisted by rotating black holes and M87*
• The generalized uncertainty principle effect in acoustic black holes
• Dilaton cosmology and the Modified Uncertainty Principle
• Primordial Power Spectra of Cosmological Fluctuations with Generalized Uncertainty Principle and Maximum Length Quantum Mechanics
• Discreteness of Space from GUP in Strong Gravitational Fields
• Generalized uncertainty principle in resonant detectors of gravitational waves
• Quantum gravity simulation by non-paraxial nonlinear optics
• Effects of the Modified Uncertainty Principle on the Inflation Parameters
• Probing the generalized uncertainty principle through quantum noises in optomechanical systems
• Black hole thermodynamics and generalized uncertainty principle with higher order terms in momentum uncertainty
• Quantum-spacetime effects on nonrelativistic Schrödinger evolution
• Modified Newton's Law of Gravitation Due to Minimal Length in Quantum Gravity
• Path integral action of a particle with the generalized uncertainty principle and correspondence with noncommutativity
• GUP-corrected black holes: Thermodynamic properties, evaporation time and shadow constraint from EHT Observations of M87* and Sgr A*
• Generalized relativistic harmonic oscillator in minimal length quantum mechanics
• A Possible Solution of the Cosmological Constant Problem based on Minimal Length Uncertainty and GW170817 and PLANCK Observations
• Indirect Probe of Quantum Gravity using Molecular Wave-packets
• Effects of the Generalized Uncertainty Principle on Quantum Tunneling
• Path integral action in the generalized uncertainty principle framework
• Formulation of the Spinor Field in the Presence of a Minimal Length Based on the Quesne-Tkachuk Algebra
• Modified entropies as the origin of generalized uncertainty principles
• Maximally localized states and quantum corrections of black hole thermodynamics in the framework of a new generalized uncertainty principle
• Constraining the generalized uncertainty principle with neutron interferometry
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Some Implications of Two Forms of the Generalized Uncertainty Principle
• Effect of the GUP on the Entropy, Speed of Sound, and Bulk to Shear Viscosity Ratio of an ideal QGP
• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
• Generalized uncertainty principle and thermostatistics: a semiclassical approach
• On the reformulation of Thomas-Fermi model to make it compatible to the Planck-scale
• An infinite square-well potential as a limiting case of a finite square-well potential in a minimal-length scenario
• The solitary solutions of nonlinear Klein-Gordon field with minimal length
• Schwinger's Model of Angular Momentum with GUP
• Path integral action for a resonant detector of gravitational waves in the generalized uncertainty principle framework
• Massless Charged Particles Tunneling Radiation from a RN-dS Horizon and the Linear and Quadratic GUP
• Hawking radiation and stability of the canonical acoustic black holes
• Uncertainty principle in quantum mechanics with Newton's gravity
• Thermodynamics of black holes and the symmetric generalized uncertainty principle
• Planck-Scale Corrections to Friedmann Equation
• Minimal length scale correction in the noise of gravitons
• Effect of RGUP on the nonlinear Klein-Gordon model with spontaneous symmetry breaking
• Deformed classical-quantum mechanics transition
• Discreteness Of Curved Space-Time From GUP
• Minimal-length quantum field theory: a first-principle approach
• Uncertainty principle from the noise of gravitons
• Photon velocity, power spectrum in Unruh effect with modified dispersion relation
• Generalized uncertainty principle in quantum cosmology for the maximally symmetric space
• Gravitational Observations and LQGUP
• Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
• Scattering and absorption by extra-dimensional black holes with GUP
• Resonant detectors of gravitational wave in the linear and quadratic generalized uncertainty principle framework
• Linear-Quadratic GUP and Thermodynamic Dimensional Reduction
• Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
• Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle
• Birth of the GUP and its effect on the entropy of the Universe in Lie-$N$-algebra
• Free Motion of a Dirac Particle with a Minimum Uncertainty in Position
• A minimal Length Uncertainty Approach to Cosmological Constant Problem
• Non-Commutative space-time and Hausdorff dimension
• Remarks on generalized uncertainty principle induced from constraint system
• Modified metrics of acoustic black holes: A review
• Loop Quantum Cosmology with a noncommutative quantum deformed photon gas
• Entropy Bound with Generalized Uncertainty Principle in General Dimensions
• Quantum Gravity Constraints on Fine Structure Constant from GUP in Braneworlds
• Transition Rate and the Photoelectric Effect in the Presence of a Minimal Length
• Big Bang Nucleosynthesis constraints on space-time noncommutativity
• Quantum tunneling driven by quintessence and the role of GUP
• Effect of Quantum Gravity on Specific Heat of Solid
• Covariant Space Time Line Elements in the Friedmann Lemaitre Robertson Walker Geometry
• A Note on Coherent States with Quantum Gravity Effects
• Thermal effects of a photon gas with a deformed Heisenberg algebra
• Thermodynamic modifications to Bardeen black holes surrounded by quintessence based on the new higher order GUP
• Particle in a cavity in one-dimensional bandlimited quantum mechanics
• From minimal-length quantum theory to modified gravity
• Exact continuity equation in a space with minimal length