Generalized uncertainty principle with maximal observable momentum and no minimal length indeterminacy

Abstract

We present a novel generalization of the Heisenberg uncertainty principle which introduces the existence of a maximal observable momentum and at the same time does not entail a minimal indeterminacy in position. The above result is an exact generalized uncertainty principle (GUP), valid at all energy scales. For small values of the deformation parameter $\beta$, our ansatz is consistent with the usual expression for GUP borrowed from string theory, doubly special relativity and other quantum gravity candidates that provide $\beta$ with a negative sign. As a preliminary analysis, we study the implications of this new model on some quantum mechanical applications and on the black hole thermodynamics.

References in corpus (44)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• The Generalized Uncertainty Principle and Black Hole Remnants
• Minimal Length Scale Scenarios for Quantum Gravity
• Generalized Lorentz invariance with an invariant energy scale
• Universality of Quantum Gravity Corrections
• Logarithmic correction to the Bekenstein-Hawking entropy
• The algebraic structure of the generalized uncertainty principle
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• General Logarithmic Corrections to Black Hole Entropy
• Doubly Special Relativity
• Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
• Black Hole Remnants and the Information Loss Paradox
• Quantum-corrected black hole thermodynamics to all orders in the Planck length
• Generalized Uncertainty Principle: Approaches and Applications
• Generalized Uncertainty Principle, Extra-dimensions and Holography
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum
• GUP parameter from quantum corrections to the Newtonian potential
• Uncertainty Relation on World Crystal and its Applications to Micro Black Holes
• Probing deformed commutators with macroscopic harmonic oscillators
• Generalized Uncertainty Principle and Corpuscular Gravity
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications
• Modified Unruh effect from Generalized Uncertainty Principle
• Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator
• Generalized Uncertainty Principle, Black Holes, and White Dwarfs: A Tale of Two Infinities
• Generalized Uncertainty Principle, Classical Mechanics, and General Relativity
• Testing of Generalized Uncertainty Principle With Macroscopic Mechanical Oscillators and Pendulums
• Casimir Effect in the Presence of Minimal Lengths
• The Casimir Effect in Minimal Length Theories based on a Generalized Uncertainity Principle
• Relativistic Generalized Uncertainty Principle
• A new holographic entropy bound from quantum geometry
• GUP parameter from Maximal Acceleration
• Phenomenology of GUP stars
• Generalized Dirac structure beyond the linear regime in graphene
• Zero Mass Remnant as an Asymptotic State of Hawking Evaporation
• A closer look at the uncertainty relation of position and momentum
• Heuristic derivation of Casimir effect in minimal length theories
• Exact and approximate solutions of Schroedinger's equation for a class of trigonometric potentials
• Entropy bound of local quantum field theory with generalized uncertainty principle
• Uncertainty principle on 3-dimensional manifolds of constant curvature
• From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks
• Heuristic derivation of the Casimir effect from Generalized Uncertainty Principle

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• The minimal length: a cut-off in disguise?
• Emergent Universe Model from Modified Heisenberg Algebra
• Quantum corrections to the thermodynamics of rotating charged BTZ black hole in gravity's rainbow
• Non-Singular Gravitational Collapse through Modified Heisenberg Algebra
• Higher-order generalized uncertainty principle applied to gravitational baryogenesis
• Constraining GUP Models Using Limits on SME Coefficients
• A framework for nonrelativistic isotropic models based on generalized uncertainty principles
• Phase transitions, critical behavior and microstructure of the FRW universe in the framework of higher order GUP
• 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
• On the algebraic approach to GUP in anisotropic space
• Finite Temperature Considerations in the Structure of Quadratic GUP-modified White Dwarfs
• Fractal properties of particle paths due to generalised uncertainty relations
• Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model
• Statistical Entropy Based on the Generalized-Uncertainty-Principle-Induced Effective Metric
• Van der Waals black holes in rainbow gravity
• Revisiting the algebraic structure of the generalized uncertainty principle
• Spontaneous Lorentz symmetry violation from infrared gravity