A Dynamical System with q-Deformed Phase Space Represented in Ordinary Variable Spaces
| Autor: | Shigefumi Naka, Haruki Toyoda, T. Takanashi |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
High Energy Physics - Theory
Physics Quantum Physics Momentum operator Free particle Physics and Astronomy (miscellaneous) Dynamical systems theory Operator (physics) Mathematical analysis FOS: Physical sciences Mathematical Physics (math-ph) Differential operator High Energy Physics - Theory (hep-th) Phase space Path integral formulation Quantum Physics (quant-ph) Dynamical system (definition) Mathematical Physics |
| Zdroj: | Progress of Theoretical Physics. 124:1019-1035 |
| ISSN: | 1347-4081 0033-068X |
| DOI: | 10.1143/ptp.124.1019 |
| Popis: | Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a difference operator instead of the differential operator. Then, using the path integral representation for such a dynamical system, we derive an effective short-time action, which contains interaction terms even for a free particle with q-deformed phase space. Analysis is also made on the eigenvalue problem for a particle with q-deformed phase space confined in a compact space. Under some boundary conditions of the compact space, there arises fairly different structures from $q=1$ case in the energy spectrum of the particle and in the corresponding eigenspace . 17page, 2 figures |
| Databáze: | OpenAIRE |
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