Perturbations of Quantum Canonical Relations and Q-Independence

  • W. A. Majewski
  • M. Marciniak
Part of the NATO ASI Series book series (NSSB, volume 324)


The aim of this note is to review some of the recent results on real and complex perturbations of quantum canonical relations. We also give a brief description of the relation between q-perturbations and q-probability calculus.


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  1. 1.
    J. Cuntz, Simple algebra generated by isometries, Comm. Math. Phys. ,57, 173 (1977).MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    D.E. Evans, On On, Publ. RIMS, Kyoto Univ. ,16, 915 (1980).MATHCrossRefGoogle Scholar
  3. 3.
    M. Bozejko and R. Speicher, An example of a generalized Brownian motion, Comm. Math. Phys. ,137, 519 (1991).MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    P.T.E. Jørgensen, L.M. Schmitt and R.F. Werner, q-canonical commutation relations and sta bility of the Cuntz algebra, Pacific J. Math (to appear).Google Scholar
  5. 5.
    W.A. Majewski, M. Marciniak, On q-perturbations of commutation relations and q-independence, Acta Phys. Polon. B ,24(4), 815 (1993).MathSciNetGoogle Scholar
  6. 6.
    D. Voiculescu, Symmetries of some reduced free product C*-algebras, in: “Operator Algebras and their Connection with Topology and Ergodic Theory”, Lect. Notes Math. 1132, Springer- Verlag, Heidelberg (1985).Google Scholar
  7. 7.
    J.S. Birman, “Braids, Links, and Mapping Class Groups”, Princeton University Press, Prince ton, New Jersey (1974).Google Scholar
  8. 8.
    A. Lerda, “Anyons”, Springer-Verlag, Heidelberg (1992).MATHGoogle Scholar
  9. 9.
    R. Haag, “Local Quantum Physics”, Springer-Verlag, Berlin, Heidelberg (1992).MATHCrossRefGoogle Scholar
  10. 10.
    G.A. Goldin, R. Menikoff and D.H. Sharp, Representations of a local current algebra in non- simply connected space and the Aharonov-Bohm effect, J. Math. Phys., ,22(8), 1664 (1981).MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    F. Wilczek, “Fractional Statistics and Anyon Superconductivity”, World Scientific, Singapore (1990).Google Scholar
  12. 12.
    R.B. Laughlin, Superconducting ground state of noninteracting particles obeying fractional statistics, Phys. Rev. Lett ,60, 2677 (1988).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • W. A. Majewski
    • 1
  • M. Marciniak
    • 2
  1. 1.Institute of Theoretical Physics and AstrophysicsGdańsk UniversityGdańskPoland
  2. 2.Institute of MathematicsGdańsk UniversityGdańskPoland

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