Minimal areas from q-deformed oscillator algebras

Abstract

On the basis of various examples we provide evidence that noncommutative spacetime involving position-dependent structure constants will give rise to deformed oscillator algebras. In turn, starting from some q-deformations of these algebras in a two-dimensional space for which the entire deformed Fock space can be constructed explicitly, we derive the commutation relations for the dynamical variables in noncommutative spacetime. We compute minimal areas resulting from these relations, i.e. finitely extended regions for which it is impossible to resolve any substructure in form of measurable knowledge. The size of the regions we find is determined by the noncommutative constant and the deformation parameter q. Any object in this type of spacetime structure has to be of membrane type or in certain limits of string type.