A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications
arXiv:1210.5334 · doi:10.1016/j.physletb.2012.10.059
Abstract
In a recent paper, we presented a nonperturbative higher order generalized uncertainty principle (GUP) that is consistent with various proposals of quantum gravity such as string theory, loop quantum gravity, doubly special relativity, and predicts both a minimal length uncertainty and a maximal observable momentum. In this Letter, we find exact maximally localized states and present a formally self-adjoint and naturally perturbative representation of this modified algebra. Then we extend this GUP to D dimensions that will be shown it is noncommutative and find invariant density of states. We show that the presence of the maximal momentum results in upper bounds on the energy spectrum of the free particle and the particle in box. Moreover, this form of GUP modifies blackbody radiation spectrum at high frequencies and predicts a finite cosmological constant. Although it does not solve the cosmological constant problem, it gives a better estimation with respect to the presence of just the minimal length.
arXiv comment15 pages, 3 figures, second part of arXiv:1110.2999, to appear in Physics Letters B
References in corpus (36)
- Hilbert Space Representation of the Minimal Length Uncertainty Relation
- Quantum gravity and minimum length
- Lorentz invariance with an invariant energy scale
- Universality of Quantum Gravity Corrections
- Discreteness of Space from the Generalized Uncertainty Principle
- The algebraic structure of the generalized uncertainty principle
- Quantum Groups, Gravity, and the Generalized Uncertainty Principle
- A proposal for testing Quantum Gravity in the lab
- Minimal Length Uncertainty Relation and Ultraviolet Regularisation
- The Effect of the Minimal Length Uncertainty Relation on the Density of States and the Cosmological Constant Problem
- Self-adjoint extensions of operators and the teaching of quantum mechanics
- Discreteness of Space from GUP II: Relativistic Wave Equations
- Signatures in the Planck Regime
- Quantum-corrected black hole thermodynamics to all orders in the Planck length
- Quantum Uncertainty in Doubly Special Relativity
- A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum
- Minimal length, maximal momentum and Hilbert space representation of quantum mechanics
- String theories with deformed energy momentum relations, and a possible non-tachyonic bosonic string
- Natural extension of the Generalised Uncertainty Principle
- The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
- Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator
- Some Aspects of Minimal Length Quantum Mechanics
- Generalised Uncertainty Principle, Remnant Mass and Singularity Problem in Black Hole Thermodynamics
- New Approach to Nonperturbative Quantum Mechanics with Minimal Length Uncertainty
- The Big-Bang Singularity in the framework of a Generalized Uncertainty Principle
- Minimal Length and Bouncing Particle Spectrum
- Generalized Uncertainty Principle, Modified Dispersion Relations and Early Universe Thermodynamics
- A class of GUP solutions in deformed quantum mechanics
- Quantum Dynamics of the Taub Universe in a Generalized Uncertainty Principle framework
- About maximally localized states in quantum mechanics
- On the modification of Hamiltonians' spectrum in gravitational quantum mechanics
- Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle
- Minimal length, maximal momentum and the entropic force law
- Generalized uncertainty principle in Bianchi type I quantum cosmology
- The minimal length uncertainty and the quantum model for the stock market
- Minimal Length and the Quantum Bouncer: A Nonperturbative Study
Cited by in corpus (63)
- Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A
- Generalized Uncertainty Principle: Approaches and Applications
- Gravitational tests of the Generalized Uncertainty Principle
- GUP parameter from quantum corrections to the Newtonian potential
- Review on Generalized Uncertainty Principle
- Probing deformed commutators with macroscopic harmonic oscillators
- Generalized uncertainty principle corrections in Rastall-Rainbow Casimir wormholes
- 30 years in: Quo vadis generalized uncertainty principle?
- Cosmological Horizons, Uncertainty Principle and Maximum Length Quantum Mechanics
- New generalized uncertainty principle from the doubly special relativity
- The extended uncertainty principle inspires the Rényi entropy
- Modelling Casimir Wormholes in Extended Gravity
- On Quantum Gravity Tests with Composite Particles
- Generalized uncertainty principle with maximal observable momentum and no minimal length indeterminacy
- Thermodynamics of the Schwarzschild and Reissner-Nordström black holes under higher-order generalized uncertainty principle
- Hubble tension bounds the GUP and EUP parameters
- Effect of the modified Heisenberg algebra on the Black hole thermodynamics
- One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum
- Spacetime singularity resolution in Snyder noncommutative space
- Influence of a Minimal Length on the Creation of Scalar Particles
- Short distance modification of the quantum virial theorem
- The minimal length: a cut-off in disguise?
- Quantum theory of the Generalised Uncertainty Principle
- Some Astrophysical Aspects of a Schwarzschild Geometry Equipped with a Minimal Measurable Length
- Black Hole Corrections due to Minimal Length and Modified Dispersion Relation
- Casimir wormhole with GUP correction in extended symmetric teleparallel gravity
- Minimum-length deformed QM/QFT, issues and problems
- Effect of minimal length uncertainty on the mass-radius relation of white dwarfs
- Minimal and maximal lengths from position-dependent noncommutativity
- New higher-order generalized uncertainty principle: Applications
- On the Chandrasekhar Limit in Generalized Uncertainty Principles
- Higher-order generalized uncertainty principle applied to gravitational baryogenesis
- Maximally localized states and quantum corrections of black hole thermodynamics in the framework of a new generalized uncertainty principle
- The minimal length and the Shannon entropic uncertainty relation
- Higher-order generalized uncertainty principle corrections to the Jeans mass
- Generalized Extended Uncertainty Principles, Liouville theorem and density of states: Snyder-de Sitter and Yang models
- Generalized uncertainty principle and thermostatistics: a semiclassical approach
- Constraining GUP Models Using Limits on SME Coefficients
- A framework for nonrelativistic isotropic models based on generalized uncertainty principles
- On the reformulation of Thomas-Fermi model to make it compatible to the Planck-scale
- Rejuvenating the hope of a swampland consistent inflated multiverse with tachyonic inflation in the high energy RS-II Braneworld
- EGUP corrected thermodynamics of RN-AdS black hole with quintessence matter
- Schwinger's Model of Angular Momentum with GUP
- Two dimensional electron gas in a non-Euclidean space
- Deformed Gazeau-Klauder Schrödinger-Cat States with Modified Commutation Relations
- Phase transitions, critical behavior and microstructure of the FRW universe in the framework of higher order GUP
- Effective models of quantum gravity induced by Planck scale modifications in the covariant quantum algebra
- Measurable Maximal Energy and Minimal Time Interval
- The new higher-order generalized uncertainty principle and primordial big bang nucleosynthesis
- The gravitational baryogenesis and a new higher-order extended uncertainty principle with parameter adaptability for the minimum length
- Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario
- Another look on the connections of Hubble tension with the Heisenberg Uncertainty Principle
- Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
- Kinetic energy properties and weak equivalence principle in a space with GUP
- Modified Brans-Dicke cosmology with Minimum Length Uncertainty
- New Non-commutative and Higher Derivatives Quantum Mechanics from GUPs
- Short Distance Modification of a Gravitational System and its Optical Analog
- Finite Temperature Considerations in the Structure of Quadratic GUP-modified White Dwarfs
- Remarks on the quasi-position representation in models of generalized uncertainty principle
- An algebraic approach to gravitational quantum mechanics
- Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation
- Maximally localized states and quantum corrections of black hole thermodynamics in the extreme case with an improved exponential GUP
- One-dimension quantum systems in the framework of the most general deformation GUP form