A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum

Abstract

We present a higher order generalized (gravitational) uncertainty principle (GUP) in the form $[X,P]=i\hslash /(1-\beta P^2)$. This form of GUP 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. We show that the presence of the maximal momentum results in an upper bound on the energy spectrum of the momentum eigenstates and the harmonic oscillator.

13 pages, 4 figures

References in corpus (18)

• Universality of Quantum Gravity Corrections
• Discreteness of Space from the Generalized Uncertainty Principle
• A proposal for testing Quantum Gravity in the lab
• Quantum-corrected black hole thermodynamics to all orders in the Planck length
• Minimal length, maximal momentum and Hilbert space representation of quantum mechanics
• 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
• 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
• Quantum Dynamics of the Taub Universe in a Generalized Uncertainty Principle framework
• 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
• Classical and quantum mechanics of the nonrelativistic Snyder model in curved space

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