Radiative neutrino mass generation within supersymmetric (SUSY) construction is studied. The mechanism is considered where the lepton number violation is originating from the soft SUSY breaking terms. This requires MSSM extensions with states around
the TeV scale. We present several explicit realizations based on extensions either by MSSM singlet or SU(2)_w triplet states. Besides some novelties of the proposed scenarios, various phenomenological implications are also discussed.
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.
