Hilbert Space Representation of the Minimal Length Uncertainty Relation
  The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements. Here we study in full detail the quantum mechanical structure which underlies this uncertainty relation. 
A. Kempf, G. Mangano, R. B. Mann