PT-symmetric noncommutative spaces with minimal volume uncertainty relations

Abstract

We provide a systematic procedure to relate a three dimensional q-deformed oscillator algebra to the corresponding algebra satisfied by canonical variables describing noncommutative spaces. The large number of possible free parameters in these calculations is reduced to a manageable amount by imposing various different versions of PT-symmetry on the underlying spaces, which are dictated by the specific physical problem under consideration. The representations for the corresponding operators are in general non-Hermitian with regard to standard inner products and obey algebras whose uncertainty relations lead to minimal length, areas or volumes in phase space. We analyze in particular one three dimensional solution which may be decomposed to a two dimensional noncommutative space plus one commuting space component and also into a one dimensional noncommutative space plus two commuting space components. We study some explicit models on these type of noncommutative spaces.

18 pages

References in corpus (6)

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Cited by in corpus (8)

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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
• Probing noncommutative theories with quantum optical experiments
• Energy corrections due to the noncommutative phase-space of the charged isotropic harmonic oscillator in a uniform magnetic field in 3D
• Dynamic noncommutative BTZ black holes