Hilbert Space Representation of the Minimal Length Uncertainty Relation
arXiv:hep-th/9412167 · doi:10.1103/PhysRevD.52.1108
Abstract
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.
21 pages, latex, epsf, 4 figures, final version which appears in Physical Review D