International Journal of Theoretical Physics

, Volume 35, Issue 11, pp 2285–2298 | Cite as

Operator structure of a nonquantum and nonclassical system

  • Diederik Aerts
  • Bart D'Hooghe
Article

Abstract

There exists a connection between the vectors of the Poincaré-sphere and the elements of the complex Hilbert space C2. This latter space is used to describe spin-1/2 measurements. We use this connection to study the intermediate cases of a more general spin-1/2 measurement model which has no representation in a Hilbert space. We construct the set of operators of this general model and investigate under which circumstances it is possible to define linear operators. Because no Hilbert space structure is possible for these intermediate cases, it can be expected that no linear operators are possible and it is shown that under very plausible assumptions this is indeed the case.

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References

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Diederik Aerts
    • 1
  • Bart D'Hooghe
    • 1
  1. 1.Department of Theoretical PhysicsVrije Universiteit BrusselBrusselsBelgium

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