Minimum-length deformed QM/QFT, issues and problems

Abstract

Using a particular Hilbert space representation of minimum-length deformed quantum mechanics, we show that the resolution of the wave-function singularities for strongly attractive potentials, as well as cosmological singularity in the framework of a minisuperspace approximation, is uniquely tied to the fact that this sort of quantum mechanics implies the reduced Hilbert space of state-vectors consisting of the functions nonlocalizable beneath the Planck length. (Corrections to the Hamiltonian do not provide such an universal mechanism for avoiding singularities.) Following this discussion, as a next step we take a critical view of the meaning of wave-function in such a quantum theory. For this reason we focus on the construction of current vector and the subsequent continuity equation. Some issues gained in the framework of this discussion are then considered in the context of field theory. Finally, we discuss the classical limit of the minimum-length deformed quantum mechanics and its dramatic consequences.

17 pages, Content extended and edited to match published version

References in corpus (35)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum gravity and minimum length
• A Generalized Uncertainty Principle in Quantum Gravity
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• On Gravity and the Uncertainty Principle
• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• Signatures in the Planck Regime
• Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
• Minimal length, maximal momentum and Hilbert space representation of quantum mechanics
• String Theory and the Space-Time Uncertainty Principle
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications
• Composite system in deformed space with minimal length
• Gauge Theories under Incorporation of a Generalized Uncertainty Principle
• Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length
• The Big-Bang Singularity in the framework of a Generalized Uncertainty Principle
• Generation of Cosmological Seed Magnetic Fields from Inflation with Cutoff
• Deformed Heisenberg algebra with minimal length and equivalence principle
• Classical and Quantum Features of the Mixmaster Singularity
• Quantum Dynamics of the Taub Universe in a Generalized Uncertainty Principle framework
• Neutrino oscillations as a novel probe for a minimal length
• Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background
• Scattering problem in deformed space with minimal length
• Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations
• PT-symmetric noncommutative spaces with minimal volume uncertainty relations
• Large extra dimensions and small black holes at the LHC
• Quantum gravity, minimum length and Keplerian orbits
• Orbital magnetic moment of the electron in the hydrogen atom in deformed space with minimal length
• Minimal Scales from an Extended Hilbert Space
• Deformed Heisenberg algebra and minimal length
• Gravity in quantum spacetime
• Implications of minimum-length deformed quantum mechanics for QFT/QG
• Quantum cosmology with a minimal length
• Field propagation in a stochastic background space: The rate of light incoherence in stellar interferometry
• Space-Time Uncertainty and Approaches to D-Brane Field Theory
• Top quark phenomenology of the ADD model and the Minimal Length Scenario

Cited by in corpus (9)

• Probing deformed commutators with macroscopic harmonic oscillators
• A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length
• On deformations of classical mechanics due to Planck-scale physics
• Black hole remnants due to Planck-length deformed QFT
• The 1.5 post-Newtonian radiative quadrupole moment in the context of a nonlocal field theory of gravity
• Extra-dimensional generalization of minimum-length deformed QM/QFT and some of its phenomenological consequences
• The Ultraviolet and Infrared Behavior of an Abelian Proca Model From the Viewpoint of a One-Parameter Extension of the Covariant Heisenberg Algebra
• Non-local imprints of gravity on quantum theory
• Lagrangian Formulation of an Infinite Derivative Real Scalar Field Theory in the Framework of the Covariant Kempf-Mangano Algebra in a $(D+1)$-dimensional Minkowski Space-time