Minimal areas from q-deformed oscillator algebras

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.

14 pages, 1 figure

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
• Generalized Deformed Commutation Relations with Nonzero Minimal Uncertainties in Position and/or Momentum and Applications to Quantum Mechanics

Cited by in corpus (5)

• q-deformed noncommutative cat states and their nonclassical properties
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• Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations
• Entangled squeezed states in noncommutative spaces with minimal length uncertainty relations
• Noncommutative quantum mechanics in a time-dependent background