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PT-symmetric non-commutative spaces with minimal volume uncertainty relations

Dey, S., Fring, A. & Gouba, L. (2012). PT-symmetric non-commutative spaces with minimal volume uncertainty relations. Journal of Physics A: Mathematical and Theoretical, 45(38), doi: 10.1088/1751-8113/45/38/385302


We provide a systematic procedure to relate a three-dimensional q-deformed oscillator algebra to the corresponding algebra satisfied by canonical variables describing non-commutative spaces. The large number of possible free parameters in these calculations is reduced to a manageable amount by imposing various different versions of -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 into a two-dimensional non-commutative space plus one commuting space component, and also into a one-dimensional non-commutative space plus two commuting space components. We study some explicit models on these types of non-commutative spaces.

Publication Type: Article
Subjects: Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
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