2013/02/19 by Sanjib Dey, Andreas Fring, Boubakeur Khantoul · 32 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Harmonic oscillator #Hermitian matrix #Mathematics #Metric (unit) #Neutrino Physics Research #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Representation (politics) #Spacetime #Type (biology) #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/46/33/335304
published in Journal of Physics A Mathematical and Theoretical 46(33), 335304 (Institute of Physics) · 14 pages, 1 figure
arxiv created 2013/02/19 · openalex publication_date 2013/07/31 · arxiv updated 2013/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate four different types of representations of deformed canonical variables leading to generalized versions of Heisenberg’s uncertainty relations resulting from noncommutative spacetime structures. We demonstrate explicitly how the representations are related to each other and study three characteristically different solvable models on these spaces, the harmonic oscillator, the manifestly non-Hermitian Swanson model and an intrinsically noncommutative model with Poschl-Teller type potential. We provide an analytical expression for the metric in terms of quantities specific to the generic solution procedure and show that when it is appropriately implemented expectation values are independent of the particular representation. A recently proposed inequivalent representation resulting from Jordan twists is shown to lead to unphysical models. We suggest an anti-PT -symmetric modification to overcome this shortcoming.