Foundations of Physics

, Volume 11, Issue 3, pp 179–203

On a quantum algebraic approach to a generalized phase space

  • D. Bohm
  • B. J. Hiley

DOI: 10.1007/BF00726266

Cite this article as:
Bohm, D. & Hiley, B.J. Found Phys (1981) 11: 179. doi:10.1007/BF00726266


We approach the relationship between classical and quantum theories in a new way, which allows both to be expressed in the same mathematical language, in terms of a matrix algebra in a phase space. This makes clear not only the similarities of the two theories, but also certain essential differences, and lays a foundation for understanding their relationship. We use the Wigner-Moyal transformation as a change of representation in phase space, and we avoid the problem of “negative probabilities” by regarding the solutions of our equations as constants of the motion, rather than as statistical weight factors. We show a close relationship of our work to that of Prigogine and his group. We bring in a new nonnegative probability function, and we propose extensions of the theory to cover thermodynamic processes involving entropy changes, as well as the usual reversible processes.

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • D. Bohm
    • 1
  • B. J. Hiley
    • 1
  1. 1.Department of Physics, Birkbeck CollegeUniversity of LondonLondonEngland

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