Phys. Rev. A 75, 066101 (2007) [5 pages]Comment on “Symplectic quantization, inequivalent quantum theories, and Heisenberg’s principle of uncertainty”Received 28 March 2006; published 22 June 2007 In M. Montesinos and G. F. Torres del Castillo Phys. Rev. A 70 032104 (2004) consider various symplectic structures on the classical phase-space of the two-dimensional isotropic harmonic oscillator. Using Dirac’s quantization condition, the authors investigate how these alternative symplectic forms affect this system’s quantization. They claim that these symplectic structures result in mutually inequivalent quantum theories. In fact, we show here that there exists a unitary map between the two representation spaces so that the various quantizations are equivalent. © 2007 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.75.066101
DOI:
10.1103/PhysRevA.75.066101
PACS:
03.65.Ca, 03.65.Ta
See AlsoOriginal Article: Merced Montesinos and G. F. Torres del Castillo, Symplectic quantization, inequivalent quantum theories, and Heisenberg’s principle of uncertainty, Phys. Rev. A 70, 032104 (2004). |
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