Quantum Mechanics on the cylinder
Jose A. Gonzalez, Mariano A del Olmo, Jaromir Tosiek
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 R2 adapted to (S1 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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