Minimal areas from<i>q</i>-deformed oscillator algebras

Abstract

We demonstrate that dynamical noncommutative space-time will give rise to\ndeformed oscillator algebras. In turn, starting from some q-deformations of\nthese algebras in a two dimensional space for which the entire deformed Fock\nspace can be constructed explicitly, we derive the commutation relations for\nthe dynamical variables in noncommutative space-time. We compute minimal areas\nresulting from these relations, i.e. finitely extended regions for which it is\nimpossible to resolve any substructure in form of measurable knowledge. The\nsize of the regions we find is determined by the noncommutative constant and\nthe deformation parameter q. Any object in this type of space-time structure\nhas to be of membrane type or in certain limits of string type.\n