Abstract
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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References
J. Cuntz, Simple algebra generated by isometries, Comm. Math. Phys. ,57, 173 (1977).
D.E. Evans, On On, Publ. RIMS, Kyoto Univ. ,16, 915 (1980).
M. Bozejko and R. Speicher, An example of a generalized Brownian motion, Comm. Math. Phys. ,137, 519 (1991).
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).
W.A. Majewski, M. Marciniak, On q-perturbations of commutation relations and q-independence, Acta Phys. Polon. B ,24(4), 815 (1993).
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).
J.S. Birman, “Braids, Links, and Mapping Class Groups”, Princeton University Press, Prince ton, New Jersey (1974).
A. Lerda, “Anyons”, Springer-Verlag, Heidelberg (1992).
R. Haag, “Local Quantum Physics”, Springer-Verlag, Berlin, Heidelberg (1992).
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).
F. Wilczek, “Fractional Statistics and Anyon Superconductivity”, World Scientific, Singapore (1990).
R.B. Laughlin, Superconducting ground state of noninteracting particles obeying fractional statistics, Phys. Rev. Lett ,60, 2677 (1988).
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Majewski, W.A., Marciniak, M. (1994). Perturbations of Quantum Canonical Relations and Q-Independence. In: Fannes, M., Maes, C., Verbeure, A. (eds) On Three Levels. NATO ASI Series, vol 324. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2460-1_43
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DOI: https://doi.org/10.1007/978-1-4615-2460-1_43
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