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Quantum Mechanics on the cylinder

Jose A. Gonzalez·Mariano A del Olmo·Jaromir Tosiek
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Abstract

A new approach to deformation quantization on the cylinder considered as phase space is presented. The method is based on the standard Moyal formalism for R^2 adapted to (S^1 x R) by the Weil--Brezin--Zak transformation. The results are compared with other solutions of this problem presented by Kasperkovitz and Peev (Ann. Phys. vol. 230, 21 (1994)0 and by Plebanski and collaborators (Acta Phys. Pol. vol. B 31}, 561 (2000)). The equivalence of these three methods is proved.

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Jose A. Gonzalez, Mariano A del Olmo, Jaromir Tosiek. 2003-06-02. Quantum Mechanics on the cylinder. https://doi.org/10.1088/1464-4266/5/3/362

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