Minimum-length deformed QM/QFT, issues and problems

Understand

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.