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

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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