Comment on ``Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty''

Details Comment on ``Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty'' Comment on ``Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty''

2006-03-28

arxiv.org/abs/quant-ph/0603259v2

Phys. Rev. A 75, 066101 (2007)

Physics

Quantum Physics

6 pages, updated version

Scientific paper

10.1103/PhysRevA.75.066101

In Phys. Rev. A 70, 032104 (2004), M. Montesinos and G. F. Torres del Castillo 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.

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