Coherent State Quantization and Moment Problem
| Autor: | J. P. Gazeau, M. C. Baldiotti, D. M. Gitman |
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| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Acta Polytechnica, Vol 50, Iss 3 (2010) |
| Druh dokumentu: | article |
| ISSN: | 1210-2709 1805-2363 |
| Popis: | Berezin-Klauder-Toeplitz (“anti-Wick”) or “coherent state” quantization of the complex plane, viewed as the phase space of a particle moving on the line, is derived from the resolution of the unity provided by the standard (or gaussian) coherent states. The construction of these states and their attractive properties are essentially based on the energy spectrum of the harmonic oscillator, that is on natural numbers. We follow in this work the same path by considering sequences of non-negative numbers and their associated “non-linear” coherent states. We illustrate our approach with the 2-d motion of a charged particle in a uniform magnetic field. By solving the involved Stieltjes moment problem we construct a family of coherent states for this model. We then proceed with the corresponding coherent state quantization and we show that this procedure takes into account the circle topology of the classical motion. |
| Databáze: | Directory of Open Access Journals |
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