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Time Automorphisms on C*-Algebras

Author

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  • R. Hilfer

    (ICP, Universität Stuttgart, Allmandring 3, 70569 Stuttgart, Germany)

Abstract

Applications of fractional time derivatives in physics and engineering require the existence of nontranslational time automorphisms on the appropriate algebra of observables. The existence of time automorphisms on commutative and noncommutative C*-algebras for interacting many-body systems is investigated in this article. A mathematical framework is given to discuss local stationarity in time and the global existence of fractional and nonfractional time automorphisms. The results challenge the concept of time flow as a translation along the orbits and support a more general concept of time flow as a convolution along orbits. Implications for the distinction of reversible and irreversible dynamics are discussed. The generalized concept of time as a convolution reduces to the traditional concept of time translation in a special limit.

Suggested Citation

  • R. Hilfer, 2015. "Time Automorphisms on C*-Algebras," Mathematics, MDPI, vol. 3(3), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:3:p:626-643:d:52720
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    References listed on IDEAS

    as
    1. Hilfer, R., 1995. "An extension of the dynamical foundation for the statistical equilibrium concept," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(1), pages 89-96.
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