2010/01/07 by Fabio Bagarello, F. Bagarello · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Algebra and Logic #Algebra over a field #Coherent states #Commutation #Mathematical model #Mathematical structure #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #State (computer science) #math-ph #math.MP
paper · pdf · doi:10.1063/1.3300804
in press in journal of mathematical physics
arxiv created 2010/01/07 · openalex publication_date 2010/02/01 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In a recent paper, Trifonov suggested a possible explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. Although being rather intriguing, in his treatment many mathematical aspects of the model have just been neglected, making most of the results of that paper purely formal. For this reason we are reconsidering the same model and we repeat and extend the same construction paying particular attention to all the subtle mathematical points. From our analysis the crucial role of Riesz bases clearly emerges. We also consider coherent states associated with the model.