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Quantum Phase Space from Schwinger’s Measurement Algebra

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Abstract

Schwinger’s algebra of microscopic measurement, with the associated complex field of transformation functions, is shown to provide the foundation for a discrete quantum phase space of known type, equipped with a Wigner function and a star product. Discrete position and momentum variables label points in the phase space, each taking \(N\) distinct values, where \(N\) is any chosen prime number. Because of the direct physical interpretation of the measurement symbols, the phase space structure is thereby related to definite experimental configurations.

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Acknowledgments

The authors wish to thank the referee of an earlier version for constructive comments.

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Authors and Affiliations

  1. Department of Mathematics, Centre for Mathematical Physics, University of Queensland, Brisbane, QLD , 4072, Australia

    P. Watson & A. J. Bracken

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  1. P. Watson
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  2. A. J. Bracken
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Correspondence to P. Watson.

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Watson, P., Bracken, A.J. Quantum Phase Space from Schwinger’s Measurement Algebra. Found Phys 44, 762–780 (2014). https://doi.org/10.1007/s10701-014-9813-1

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  • DOI: https://doi.org/10.1007/s10701-014-9813-1

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