Publication: Canonical transformations to action and phase-angle variables and phase operators
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1993-07
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American Physical Society
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Abstract
The well-known difficulties of defining a phase operator of an oscillator are considered from the point of view of the canonical transformation to action and phase-angle variables. This transformation turns out to be nonbijective, i.e., it is not a one-to-one onto mapping. In order to make possible the unitarity of its representations in quantum optics we should enlarge the Hilbert space of the problem. In this enlarged space we find a phase operator that, after projection, reproduces previous candidates to represent a well-behaved phase operator in the quantum domain.
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© 1993 The American Physical Society.
The authors would like to thank Professor A. Galindo and Professor R. Tanas for a critical reading of the manuscript and useful comments. They are grateful as well to Professor J.F. Carinena for helpful and enlightening discussions of some rather technical points. Finally, they benefited from the continuous interest and advice of Professor E. Bernabeu.
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