Foundations of Physics

, Volume 44, Issue 7, pp 762–780 | Cite as

Quantum Phase Space from Schwinger’s Measurement Algebra

  • P. Watson
  • A. J. Bracken


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.


Schwinger’s measurement algebra Discrete quantum phase space Star product Wigner function 



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


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Centre for Mathematical PhysicsUniversity of QueenslandBrisbaneAustralia

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