Time Automorphisms on C*-Algebras

R. Hilfer
Additional contact information
R. Hilfer: ICP, Universität Stuttgart, Allmandring 3, 70569 Stuttgart, Germany

Mathematics, 2015, vol. 3, issue 3, 1-18

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.

Keywords: fractional time derivatives; fractional time evolution; C*-algebra; local stationarity; irreversibility problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/3/3/626/pdf (application/pdf)
https://www.mdpi.com/2227-7390/3/3/626/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:3:y:2015:i:3:p:626-643:d:52720

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().