A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications

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.

15 pages, 3 figures, second part of arXiv:1110.2999, to appear in Physics Letters B

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• 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
• Short distance modification of the quantum virial theorem
• The minimal length: a cut-off in disguise?
• Black Hole Corrections due to Minimal Length and Modified Dispersion Relation
• Casimir wormhole with GUP correction in extended symmetric teleparallel gravity
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• On the Chandrasekhar Limit in Generalized Uncertainty Principles
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• Generalized Extended Uncertainty Principles, Liouville theorem and density of states: Snyder-de Sitter and Yang models
• EGUP corrected thermodynamics of RN-AdS black hole with quintessence matter
• Constraining GUP Models Using Limits on SME Coefficients
• Rejuvenating the hope of a swampland consistent inflated multiverse with tachyonic inflation in the high energy RS-II Braneworld
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• 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
• Another look on the connections of Hubble tension with the Heisenberg Uncertainty Principle
• 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
• Modified Brans-Dicke cosmology with Minimum Length Uncertainty
• Finite Temperature Considerations in the Structure of Quadratic GUP-modified White Dwarfs
• New Non-commutative and Higher Derivatives Quantum Mechanics from GUPs
• 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
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