Minimal areas from q-deformed oscillator algebras

TL;DR

This paper explores how q-deformed oscillator algebras in noncommutative space-time lead to minimal measurable areas, indicating a fundamental limit to spatial resolution influenced by deformation parameters.

Contribution

It derives explicit commutation relations and minimal area bounds from q-deformed oscillator algebras in noncommutative space-time, linking algebraic deformation to physical spatial limits.

Findings

Minimal areas depend on noncommutative constant and q-deformation parameter.

Objects in this space-time are of membrane or string type.

Explicit construction of deformed Fock space for two-dimensional case.

Abstract

We demonstrate that dynamical noncommutative space-time 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 space-time. 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 space-time structure has to be of membrane type or in certain limits of string type.