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Mathematics 2015, 3(3), 626-643; doi:10.3390/math3030626

Time Automorphisms on C*-Algebras

ICP, Universität Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
Academic Editor: Hari M. Srivastava
Received: 24 March 2015 / Revised: 24 June 2015 / Accepted: 2 July 2015 / Published: 16 July 2015
(This article belongs to the Special Issue Recent Advances in Fractional Calculus and Its Applications)
View Full-Text   |   Download PDF [292 KB, uploaded 16 July 2015]

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. View Full-Text
Keywords: fractional time derivatives; fractional time evolution; C*-algebra; local stationarity; irreversibility problem fractional time derivatives; fractional time evolution; C*-algebra; local stationarity; irreversibility problem
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Hilfer, R. Time Automorphisms on C*-Algebras. Mathematics 2015, 3, 626-643.

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