City Research Online

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), article number 385302. doi: 10.1088/1751-8113/45/38/385302

Abstract

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
SWORD Depositor:
[thumbnail of 1205.2291.pdf]
Preview
PDF
Download (217kB) | Preview

Export

Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login