Foundations of Physics 44 (7):762-780 (2014)

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
Keywords Schwinger’s measurement algebra  Discrete quantum phase space  Star product  Wigner function
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DOI 10.1007/s10701-014-9813-1
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Schwinger Algebra for Quaternionic Quantum Mechanics.L. P. Horwitz - 1997 - Foundations of Physics 27 (7):1011-1034.

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